Administrator
Assignment busshw1 due 10/15/2012 at 01:04pm EDT
math111
Match the Lines L1 (blue), L2 ( red) and L3 (green) with the
slopes by placing the letter of the slopes next to each set listed
below:
1. (1 pt) Library/Rochester/setVectors0Introduction/ur vc 0 2.pg
If the distance from the town of Bree to Weathertop is 6 miles
on a 45 degree upward slope, what is the elevation gain (omit
units)?
1.
2.
3.
A.
B.
C.
Correct Answers:
• 4.24264068711928
2. (1 pt) Library/Rochester/setVectors0Introduction/ur vc 0 1.pg
If Tom Bombadil’s house is 5 miles east of Hobbiton and 12
miles south, what is the straight line distance (omit units)?
The slope of line L1
The slope of line L3
The slope of line L2
m = −0.5
m=0
m=2
Correct Answers:
• A
• C
• B
Correct Answers:
• 13
3. (1 pt) Library/Rochester/setAlgebra14Lines/faris1.pg
The demand equation for a certain product is given by p =
136 − 0.07x , where p is the unit price (in dollars) of the product and x is the number of units produced. The total revenue
obtained by producing and selling x units is given by R = xp.
5. (1 pt) Library/Rochester/setAlgebra14Lines/lh2-1 5.pg
Find an equation y = mx +b for the line whose graph is sketched
Determine prices p that would yield a revenue of 6630 dollars.
Lowest such price =
Highest such price =
Correct Answers:
• 3.5027132353616
• 132.497286764638
4. (1 pt) Library/Rochester/setAlgebra14Lines/lh2-1 1 mo.pg
The slope m equals
.
The y-intercept b equals
.
Correct Answers:
• 0.5
• -1
6. (1 pt) Library/Rochester/setAlgebra14Lines/srw1 10 7.pg
The equation of the line with slope 3 that goes through the
point (5, 5) can be written in the form y = mx + b where m is:
and where b is:
Correct Answers:
1
• 3
• -10
13. (1 pt) Library/Rochester/setAlgebra14Lines/sw2 4 5.pg
The equation of the line that goes through the points (−5, −10)
and (7, 6) can be written in the form y = mx + b where its slope
m is:
7. (1 pt) Library/Rochester/setAlgebra14Lines/slope from pts var.pg
Find the slope of the line passing through the points (a, 2a − 1)
and (a + h, 2(a + 3h) − 1).
Correct Answers:
The slope is
• 1.33333333333333
14. (1 pt) Library/Rochester/setAlgebra14Lines/srw1 10 8.pg
The equation of the line with slope 4 that goes through the
point (−9, 4) can be written in the form y = mx + b where m is:
Correct Answers:
• 6
8. (1 pt) Library/Rochester/setAlgebra14Lines/sApB 21-26.pg
A line through (−3, 6) with a slope of 5 has a y-intercept at
and where b is:
Correct Answers:
Correct Answers:
• 4
• 40
• 21
9. (1 pt) Library/Rochester/setAlgebra14Lines/sw2 4 41.pg
Find the slope and y-intercept of the line 6x + 4y = 0.
the slope of the line is:
the y-intercept of the line is:
15. (1 pt) Library/Rochester/setAlgebra14Lines/sw2 4 11.pg
Find an equation y = mx +b for the line whose graph is sketched
Correct Answers:
• -1.5
• 0
10. (1 pt) Library/Rochester/setAlgebra14Lines/sApB 31-36a.pg
An equation of a line through (4, 5) which is perpendicular to
the line y = 4x + 3 has slope:
and y-intercept at:
Correct Answers:
• -0.25
• 6
11. (1 pt) Library/Rochester/setAlgebra14Lines/sw2 4 39.pg
Find the slope and y-intercept of the line x + y = 5.
the slope of the line is:
the y-intercept of the line is:
The number m equals
The number b equals
Correct Answers:
• -1
• 5
.
.
Correct Answers:
• 0.5
• 3
12. (1 pt) Library/Rochester/setAlgebra14Lines/sw2 4 19.pg
The equation of the line that goes through the points (3, 4) and
(6, 5) can be written in the form y = mx + b where m is:
and b is:
16. (1 pt) Library/Rochester/setAlgebra14Lines/pts to gen.pg
The equation of the line that goes through the points (3, −6) and
(−4, 10) can be written in general form Ax + By +C = 0 where
A=
B=
C=
Correct Answers:
• 0.333333333333333
• 3
Correct Answers:
2
The slope m equals
.
The y-intercept b equals
• 16
• 7
• -6
.
Correct Answers:
• -0.5
• 2
17. (1 pt) Library/Rochester/setAlgebra14Lines/sApB 31-36.pg
An equation of a line through (1, 1) which is perpendicular to
the line y = 2x + 1 has slope:
22. (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh3-1 40.pg
and y-intercept at:
Correct Answers:
• -0.5
• 1.5
18. (1 pt) Library/Rochester/setAlgebra14Lines/srw1 10 9.pg
The equation of the line with slope −4 that goes through the
point (6, −2) can be written in the form y = mx + b where m is:
and where b is:
Correct Answers:
• -4
• 22
19. (1 pt) Library/Rochester/setAlgebra14Lines/srw1 10 19a.pg
The equation of the line that goes through the point (6, 7) and is
perpendicular to the line 3x + 5y = 5 can be written in the form
y = mx + b where m is:
and where b is:
The graph of a quadratic function f (x) is shown above. It has
a vertex at (−2, −4) and passes the point (0, 0). Find the quadratic function.
f (x) =
Correct Answers:
• 1.66666666666667
• -3
Correct Answers:
• (x+2)**2-4
20. (1 pt) Library/Rochester/setAlgebra14Lines/lh2-1 9.pg
Find an equation y = mx +b for the line whose graph is sketched
23. (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh3-1 4-6.pg
Attention: you are allowed to submit your answer two times
only for this problem!
Identify the graphs A (blue), B (red) and C (green):
3
is the graph of the function f (x) = 4 − x2
is the graph of the function g(x) = 2 − (x − 6)2
is the graph of the function h(x) = (x + 4)2 − 6
Correct Answers:
• C
• A
• B
24. (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh3-1 1-3.pg
Attention: you are allowed to submit your answer two times
only for this problem!
Identify the graphs A (blue), B (red) and C (green):
is the graph of the function f (x) = −(x − 5)2
is the graph of the function g(x) = −(x − 2)2 − 5
is the graph of the function h(x) = (x + 5)2 − 2
Correct Answers:
• C
• B
• A
26. (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh3-1 79.pg
The revenue function in terms of the number of units sold ,x, is
given as
Identify the graphs A (blue), B (red) and C (green):
is the graph of the function f (x) = (x − 5)2
is the graph of the function g(x) = (x + 6)2
is the graph of the function h(x) = x2 − 5
R = 380x − 0.5x2
where R is the total revenue in dollars. Find the number of units
sold x that produces a maximum revenue?
Your answer is x =
What is the maximum revenue?
Correct Answers:
• A
• B
• C
Correct Answers:
• 380
• 72200
25. (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh3-1 6-8.pg
Attention: you are allowed to submit your answer two times
only for this problem!
27. (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh3-1 42.pg
4
Note:
right.
Be careful, You only have TWO chances to get them
1.
2.
3.
4.
x + 7 = y2
7x = y2
x2 + 5y = 6
6 + x = y3
Correct Answers:
•
•
•
•
The graph of a quadratic function f (x) is shown above. It has
a vertex at (2, 0) and passes the point (0, 8). Find the quadratic
function.
f (x) =
No
No
Yes
Yes
30. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/c0s5p4.pg
Determine which of the following statements are true and which
are false. Enter the T or F in front of each statement.
Remember that x ∈ (−1, 1) is the same as −1 < x < 1
and x ∈ [−1, 1] means −1 ≤ x ≤ 1.
Correct Answers:
• 2*(x-2)**2
28. (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh3-1 38.pg
1. The function sin(x) on the domain x ∈ (−π, π) has at
least one input which produces a smallest output value.
2. The function sin(x) on the domain x ∈ [−π, π] has at
least one input which produces a largest output value.
3. The function sin(x) on the domain x ∈ [−π, π] has at
least one input which produces a smallest output value.
4. The function f (x) = x3 with domain x ∈ [−3, 3] has at
least one input which produces a smallest output value.
5. The function f (x) = x3 with domain x ∈ (−3, 3) has at
least one input which produces a smallest output value.
Correct Answers:
•
•
•
•
•
The graph of a quadratic function f (x) is shown above. It has
a vertex at (1, 2) and passes the point (0, 1). Find the quadratic
function.
f (x) =
T
T
T
T
F
Correct Answers:
• -(x-1)**2+2
31.
29. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/2.pg
Enter Yes or No in each answer space below to indicate whether
the corresponding equation defines y as a function of x.
3 30a.pg
5
(1 pt) Library/Rochester/setAlgebra16FunctionGraphs/lh2-
Consider the function whose graph is sketched:
33.
(1 pt) Library/Rochester/setAlgebra16FunctionGraphs/lh2-
3 48a.pg
Consider the function whose graph is sketched:
Find the intervals over which the function is strictly increasing
or decreasing. Express your answer in interval notation.
The interval over which the function is strictly increasing:
Find the intervals over which the function is strictly increasing or strictly decreasing. Express your answer in
interval notation.
The interval over which the function is strictly decreasing:
Correct Answers:
• [3,infinity)
• (-infinity,3]
The interval over which the function is strictly increasing:
The interval over which the function is strictly decreasing:
32. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/c0s5p3.pg
Determine which of the following statements are true and which
are false. Enter the T or F in front of each statement.
Remember that x ∈ (−1, 1) is the same as −1 < x < 1
and x ∈ [−1, 1] means −1 ≤ x ≤ 1.
Correct Answers:
• [4,infinity)
• (-infinity,-4]
1. The function sin(x) on the domain x ∈ (−π/2, π/2)
has at least one input which produces a smallest output
value.
2. The function f (x) = x2 with domain x ∈ [−3, 3] has at
least one input which produces a largest output value.
3. The function sin(x) on the domain x ∈ [−π/2, π/2] has
at least one input which produces a smallest output
value.
4. The function f (x) = x2 with domain x ∈ (−3, 3) has at
least one input which produces a smallest output value.
5. The function sin(x) on the domain x ∈ (−π/2, π/2) has
at least one input which produces a largest output value.
34. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/sw4 2 7.pg
Consider the function given in the following graph.
Correct Answers:
•
•
•
•
•
F
T
T
T
F
What is its domain?
6
3. 2|x| + y = 8
4. 1 + x = y3
What is its range?
Note: Write the answer in interval notation.
Correct Answers:
Correct Answers:
• [-3,3]
• [-1,2]
•
•
•
•
35. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/jj1.pg
Consider the function shown in the following graph.
Yes
No
Yes
Yes
38. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/4.pg
Enter Yes or No in each answer space below to indicate whether
the corresponding equation defines y as a function of x.
Note: Be careful, You only have TWO chances to get them
right.
1.
2.
3.
4.
2|x| + y = 8
6x = y2
x + 6 = y2
x2 + 2y = 7
Correct Answers:
•
•
•
•
Where is the function decreasing?
Yes
No
No
Yes
Note: use interval notation to enter your answer.
39.
Correct Answers:
• (-3,5)
(1
pt)
Library/Rochester/setAlgebra16FunctionGraphs-
/ns1 1 45.pg
36. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/5.pg
Enter Yes or No in each answer space below to indicate whether
the corresponding equation defines y as a function of x.
Note: Be careful, You only have TWO chances to get them
right.
1.
2.
3.
4.
2|x| + y = 1
8 + x = y3
x + 10 = y2
10x = y2
Write the equation describing the graph above:
Correct Answers:
•
•
•
•
Yes
Yes
No
No
for x in the interval [
to
]
for x in the interval [
to
]
f (x) =
Correct Answers:
37. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/6.pg
Enter Yes or No in each answer space below to indicate whether
the corresponding equation defines y as a function of x.
Note: Be careful, You only have TWO chances to get them
right.
•
•
•
•
•
•
1. x2 + 5y = 6
2. x + 3 = y2
7
0*(x + 5)
-5
2
-3*(x - 2)
2
3
+ 5
+ 5
40.
(1
/sw4 2 41 51.pg
pt)
42. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/sw4 2 1.pg
For the function h(x) given in the graph
Library/Rochester/setAlgebra16FunctionGraphs-
Enter Yes or No in each answer space below to indicate whether
the corresponding equation defines y as a function of x.
Note: Be careful, You only have TWO chances to get them
right.
1.
2.
3.
4.
x + 1 = y2
x2 + 5y = 7
9 + x = y3
1x = y2
Correct Answers:
•
•
•
•
No
Yes
Yes
No
its domain is
;
its range is
;
Write the answer in interval notation.
and then enter the corresponding function value in each answer
space below:
41. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/ns1 1 2.pg
1.
2.
3.
4.
h(1)
h(−2)
h(−1)
h(0)
Correct Answers:
• [-3,3]
• [-2,2]
• 0
• 1
• -1
• -2
43.
(1 pt) Library/Rochester/setAlgebra16FunctionGraphs/c2s2p59 72/c2s2p59 72.pg
Given the graphs of f (in blue) and g (in red) to the left answer
these questions:
Match the functions with their graphs. Enter the letter of the
graph below which corresponds to the function. (Click on image for a larger view )
1. Piecewise fucntion : f (x) = −1, if x < 2 and f (x) =
1, if x ≥ 2
2. Piecewise fucntion : f (x) = 2, if x ≤ −1 and f (x) =
x2 , if x > −1
3. Piecewise fucntion : f (x) = x, if x ≤ 0 and f (x) = x +
1, if x > 0
4. Piecewise fucntion : f (x) = 1 − x, if x < −2 and f (x) =
4, if x ≥ −2
1. What is the value of f at -5?
2. For what values of x is f (x) = g(x): Separate answers
by spaces (e.g “ 5 7”)
3. Estimate the solution of the equation g(x) = −5
4. On what interval is the function f decreasing? (Separate answers by a space: e.g. “-2 4”)
Correct Answers:
•
•
•
•
3
-3 2
5
-5 1
A
8
B
C
D
Correct Answers:
• D
• B
• A
• C
44.
(1
pt)
Library/Rochester/setAlgebra17FunComposition-
/srw2 8 45 mo.pg
Express the function h(x) = (x + 3)6 in the form f ◦ g. If
f (x) = x6 , find the function g(x).
Your answer is g(x)=
,
(1
pt)
g(x) f (x)
(g(x))2
( f (x))2
g( f (x))
A.
B.
C.
D.
2 + x3
1 + 2x3 + x6
1 + 2x + x2
1 + x + x3 + x4
Correct Answers:
•
•
•
•
Correct Answers:
• x + 3
45.
1.
2.
3.
4.
D
C
B
A
Library/Rochester/setAlgebra17FunComposition-
/s0 1 84a.pg
49.
Let f (x) = 2x + 4 and g(x) = 5x2 + 3x.
After simplifying,
( f g)(x) =
(1
pt)
Library/Rochester/setAlgebra17FunComposition-
/sw4 7 23.pg
Click on the graph to view a larger graph
For the function f (x) and g(x) are given in the following graph.
Correct Answers:
• 10*xˆ3+26*xˆ2+12*x
46. (1 pt) Library/Rochester/setAlgebra17FunComposition/pcomp.pg
Given that f (x) = x2 − 4x and g(x) = x − 9, calculate
(a) f ◦ g(x)=
,
(b) g ◦ f (x)=
,
(c) f ◦ f (x)=
,
(d) g ◦ g(x)=
,
Correct Answers:
• (x+-9)**2+-4*(x+-9)
• x**2+-4*x+-9
• (x**2+-4*x)**2+-4*(x**2+-4*x)
• x+2*-9
47.
(1
pt)
Find the corresponding function values.
Library/Rochester/setAlgebra17FunComposition-
1. f (g(0))
2. f (g(2))
/ur fn 2 10.pg
1
7
Let f (x) =
and g(x) = + 7.
x−7
x
Then ( f ◦ g)(x) =
,
(g ◦ f )(x) =
.
Correct Answers:
• -1
• 4
Correct Answers:
• x/7
• 7*x-7*7+7
50. (1 pt) Library/Rochester/setAlgebra17FunComposition/s0 1 83.pg
Let f (x) = 2x + 4 and g(x) = 5x2 + 3x.
( f + g)(4) =
48. (1 pt) Library/Rochester/setAlgebra17FunComposition/c0s1p9.pg
This problem gives you some practice identifying how more
complicated functions can be built from simpler functions.
Correct Answers:
Let f (x) = x3 + 1and let g(x) = x + 1. Match the functions
defined below with the letters labeling their equivalent expressions.
• 104
9
51.
(1
pt)
55. (1 pt) Library/Rochester/setAlgebra15Functions/s0 1 2a.pg
f (1 + h) − f (1)
Let f (x) = 3x2 + 5x + 3 and let q(h) =
. Then
h
q(0.01) =
Library/Rochester/setAlgebra17FunComposition-
/ur fn 2 5.pg
1
1
and g(x) =
.
x−3
x−1
Then the domain of f ◦ g is equal to all reals except for two
values, a and b with a < b and
a=
b=
Let f (x) =
Correct Answers:
• 11.03
56. (1 pt) Library/Rochester/setAlgebra15Functions/lh2-2 36.pg
Given the function
−2x2 + 8 if x < 1
f (x) =
−4x2 + 8 if x ≥ 1
Correct Answers:
• 1
• 1.33333333333333
52.
(1
pt)
Calculate the following values:
f (−2) =
f (1) =
f (2) =
Library/Rochester/setAlgebra17FunComposition-
/ur fn 2 2.pg
This problem tests calculating new functions from old ones.
From the table below calculate the quantities asked for:
x
−20
−23
f (x) −16421 −24887
g(x)
8421
12720
3
47
−20
−2
15
−23 6539
15 −3164
Correct Answers:
• 0
• 4
• -8
47
205483
−101660
57. (1 pt) Library/Rochester/setAlgebra15Functions/srw2 1 19.pg
Given the function f (x) = 4|x − 8|, calculate the following values:
f (0) =
f (2) =
f (−2) =
f (x + 1) =
f (x2 + 2) =
Note: In your answer, you may use abs(g(x)) for |g(x)|.
( f g)(−2) =
( f + g)(3) =
g( f (3)) =
Correct Answers:
• -345
• 27
• -101660
Correct Answers:
• 32
• 24
• 40
• 4*abs(x+1-8)
• 4*abs(x**2+2-8)
53. (1 pt) Library/Rochester/setAlgebra24Variation/lh3-5 62.pg
A company has found that the demand for its product varies inversely as the price of the product. When the price x is 4.75
dollars, the demand y is 550 units. Find a mathematical model
that gives the demand y in terms of the price x in dollars.
Your answer is y =
Approximate the demand when the price is 9 dollars.
Your answer is:
58. (1 pt) Library/Rochester/setAlgebra15Functions/jay4.pg
An open box is to be made from a flat square piece of material
16 inches in length and width by cutting equal squares of length
x from the corners and folding up the sides.
Write the volume V of the box as a function of x. Leave it as a
product of factors; you do not have to multiply out the factors.
V=
Correct Answers:
• 4.75*550/x
• 290.277777777778
If we write the domain of the box as an open interval in the
form (a, b), then what is a?
a=
and what is b?
b=
54. (1 pt) Library/Rochester/setAlgebra24Variation/joint.pg
Suppose p varies jointly as the square of q and the cube root of
r. If p = 8 when q = 3 and r = 4, what is p if q = 15 and r = 6?
p=
Correct Answers:
• ((16-2x)(16-2x)x)
• 0
• 8
Correct Answers:
• 228.942848510666
10
• E
• E
59. (1 pt) Library/Rochester/setAlgebra15Functions/p2.pg
The domain of the function
r
4x
x2 − 1
63. (1 pt) Library/Rochester/setAlgebra15Functions/srw2 1 33.pg
Given the function f (x) = 3 + 5x2 , calculate the following values:
f (a) =
f (a + h) =
f (a + h) − f (a)
=
h
is
Write the answer in interval notation.
Note: If the answer includes more than one interval write the
intervals separated by the union symbol, U. If needed enter −∞
as - infinity and ∞ as infinity .
Correct Answers:
• 5*a**2+3
• 5*(a+h)**2+3
• 5*2*a+5*h
Correct Answers:
• (-1,0] U (1,infinity)
60. (1 pt) Library/Rochester/setAlgebra15Functions/p4.pg
Find domain and range of the function
64. (1 pt) Library/Rochester/setAlgebra15Functions/p1.pg
The domain of the function
1
√
18x + 18
15x2 − 2
Domain:
Range:
Write the answer in interval notation.
Note: If the answer includes more than one interval write the
intervals separated by the union symbol, U. If needed enter −∞
as - infinity and ∞ as infinity .
is
Write the answer in interval notation.
Note: If the answer includes more than one interval write the
intervals separated by the union symbol, U. If needed enter −∞
as - infinity and ∞ as infinity .
Correct Answers:
• (-1,infinity)
Correct Answers:
• (-infinity,infinity)
• [-2,infinity)
65. (1 pt) Library/Rochester/setAlgebra15Functions/sw4 1 31.pg
Let f (x) = 2. Calculate the following values:
f (a) =
f (a + h) =
f (a + h) − f (a)
=
for h 6= 0
h
61. (1 pt) Library/Rochester/setAlgebra15Functions/srw2 1 45.pg
The domain of the function
8x + 14, −8 ≤ x ≤ 3
Correct Answers:
• 2
• 2
• 0
is
.
Write the answer in interval notation.
Note: If the answer includes more than one interval write the
intervals separated by the union symbol, U. If needed enter −∞
as - infinity and ∞ as infinity .
66. (1 pt) Library/Rochester/setAlgebra15Functions/box.pg
An open box is to be made from a flat piece of material 13 inches
long and 5 inches wide by cutting equal squares of length x from
the corners and folding up the sides.
Correct Answers:
• [-8,3]
62. (1 pt) Library/Rochester/setAlgebra15Functions/s0 1 77-82.pg
For each of the following functions, decide whether it is even,
odd, or neither. Enter E for an EVEN function, O for an ODD
function and N for a function which is NEITHER even nor odd.
Note: You will only have four attempts to get this problem
right!
1.
2.
3.
4.
Write the volume V of the box as a function of x. Leave it
as a product of factors, do not multiply out the factors.
V (x) =
If we write the domain of V (x) as an open interval in the form
(a, b), then what is a?
a=
and what is b?
b=
f (x) = x2 + 3x4 + 2x3
f (x) = x3 + x5 + x3
f (x) = x2 − 6x4 + 3x2
f (x) = x−6
Correct Answers:
• ((13-2x)(5-2x)x)
• 0
• 2.5
Correct Answers:
• N
• O
11
•
•
•
•
•
•
•
67. (1 pt) Library/FortLewis/Algebra/5-2-Linear-expressions/MCH15-2-44-Linear-expressions.pg
Is the expression 3xy + 2x + 2 − 11y linear in the variable y? If
it is linear, enter the slope. If it is not linear, enter NO.
Correct Answers:
Linear
Linear
Linear
Linear
Linear
Not Linear
Not Linear
70. (1 pt) Library/FortLewis/Algebra/5-2-Linear-expressions/MCH15-2-40-Linear-expressions.pg
• 3 * x - 11
Is the expression ax2 + 2x + 4 linear in the variable x? If it is
linear, enter the slope. If it is not linear, enter NO.
68. (1 pt) Library/FortLewis/Algebra/5-2-Linear-expressions/MCH15-2-23b-Linear-expressions.pg
Find an equation for of each of the lines in the figure.
Correct Answers:
• NO
Line A (in red) has equation y =
71. (1 pt) Library/FortLewis/Algebra/5-4-Equations-for-lines/MCH15-4-58-Equations-for-lines.pg
Line B (in blue) has equation y =
Write the equation for the line 2x + 5y = 8 in the form
y = mx + b, and enter it in this form.
Correct Answers:
• y = (-2/5) x + 8/5
72. (1 pt) Library/FortLewis/Algebra/9-3-Completing-the-square/MCH1-9-3-24-Completing-the-square.pg
Solve the quadratic equation x2 − 8x − 3 = 0. If there is more
than one correct answer, enter your answers as a comma separated list. If there are no solutions, enter NONE.
x=
Correct Answers:
• 8.3589, -0.358899
73. (1 pt) Library/FortLewis/Algebra/9-3-Completing-the-square/MCH1-9-3-38-Completing-the-square.pg
(Click on graph to enlarge)
(a) Complete the square by writing 3x2 + 24x + 1 in the form
a(x − h)2 + k. Note: the numbers a, h and k can be positive or
negative.
Correct Answers:
• -0.5*x+6
• 1.5*x+1
69. (1 pt) Library/FortLewis/Algebra/5-2-Linear-expressions/MCH15-2-01-Linear-expressions.pg
3x2 + 24x + 1 =
·
2
+
Are the expressions linear or not?
?
?
?
?
?
?
?
?
1.
2.
3.
4.
5.
6.
7.
8.
5r2 + 2
(3a + 1)/4
5t − 8
6r + r − 1
42 + (1/3)x
6A − 3(1 − 3A)
(3a + 1)/a
5x + 1
(b) Solve the equation 3x2 + 24x + 1 = 0 by completing the
square or using the quadratic formula. If there is more than one
correct answer, enter your answers as a comma separated list. If
there are no solutions, enter NONE.
x=
Correct Answers:
•
•
•
•
Correct Answers:
• Not Linear
12
3
x+4
-47
-0.041886, -7.95811
74. (1 pt) Library/FortLewis/Algebra/9-3-Completing-the-square/MCH1-9-3-44-Completing-the-square.pg
77. (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions/MCH1-9-2-36-Quadratic-expressions.pg
(a) Complete the square by writing 2x2 + 2x + 3 in the form
a(x − h)2 + k. Note: the numbers a, h and k can be positive or
negative.
Put the function y = 5x2 + 40x + 17 in vertex form f (x) =
a(x − h)2 + k and determine the values of a, h, and k.
2x2 + 2x + 3 =
2
·
a=
+
h=
(b) Solve the equation 2x2 + 2x + 3 = 0 by completing the
square or using the quadratic formula. If there is more than one
correct answer, enter your answers as a comma separated list. If
there are no solutions, enter NONE.
k=
Correct Answers:
• 5
• -4
• -63
x=
78. (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions/MCH1-9-2-46-Quadratic-expressions.pg
Correct Answers:
• 2
• x+1/2
• 2.5
• NONE
Suppose y = 2x2 + 24x − 74. In each part below, if there is
more than one correct answer, enter your answers as a comma
separated list. If there are no correct answers, enter NONE.
75. (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions/MCH1-9-2-26-Quadratic-expressions.pg
Write the expression
b)(cx + d).
x2
(a) Find the y-intercept(s).
y=
+ 11x + 30 in factored form k(ax +
(b) Find the x-intercept(s).
x=
x2 + 11x + 30 =
Correct Answers:
• (x+5)(x+6)
Correct Answers:
• -74
• 2.544, -14.544
76.
(1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions/MCH1-9-2-12-Quadratic-expressions.pg
The quadratic expression (x − 3)2 − 36 is written in vertex form.
79. (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions/MCH1-9-2-54-Quadratic-expressions.pg
(a) Write the expression in standard form ax2 + bx + c.
Find the minimum and maximum value of the function y =
(x − 2)2 + 9. Enter infinity or -infinity if the function never stops
increasing or decreasing.
(b) Write the expression in factored form k(ax + b)(cx + d).
Maximum value =
Minimum value =
Correct Answers:
(c) Evaluate the expression at x = 0 using each of the three
forms, compare the results, and enter your answer below.
• inf
• 9
80.
(1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions-
/MCH1-9-2-10-Quadratic-expressions.pg
The height of a right triangle is 7 feet more than three times the
length of its base. Express the area of the triangle as a function
of the length of its base, x, in feet.
(d) Evaluate the expression at x = 5 using each of the three
forms, compare the results, and enter your answer below.
Correct Answers:
• xˆ2-6*x-27
• (x+3) (x-9)
• -27
• -32
f (x) =
Correct Answers:
• x*(3*x+7)/2
13
square feet
81.
85. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 22 mo.pg
Evaluate the limit
(1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions-
/MCH1-9-2-02-Quadratic-expressions.pg
s3 − 1
s→1 s2 − 1
lim
Find a possible formula for the quadratic function in
the graph.
f (x) =
Correct Answers:
• ((1)ˆ2+1 +1)/(1+1)
86. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 27 mo.pg
Evaluate the limit
16 − s
√
lim
s→16 4 − s
Correct Answers:
Correct Answers:
• -(x+2)*(x-3)
82.
• 8
(1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions-
87. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 48a.pg
Evaluate the limits. If a limit does not exist, enter ”DNE”.
|x + 6|
lim
=
x→−6+ x + 6
|x + 6|
lim
=
x→−6− x + 6
|x + 6|
=
lim
x→−6 x + 6
/MCH1-9-2-50-Quadratic-expressions.pg
Find the vertex of the parabola y = 6x + 7 − x2 . Enter your
answer as a point (h, k), including the parentheses.
The vertex is at the point
Correct Answers:
• (3,16)
Correct Answers:
• 1
• -1
• DNE
83. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 27.pg
Evaluate the limit
49 − b
√
lim
b→49 7 − b
88. (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 13.pg
The main theorem of Ste 2.3 tells us that many functions are
continuous so that their limits can be evaluated by direct substitution. Calculate the following limits by direct substitution,
making use of this big theorem from Ste 2.3.
(a + 7)4
lim
=
lim y3 (5 − 3y2 ) =
lim 2x3 − 4x − 10 =
a→−10 a + 1
y→−2
x→3
r
q
13 − s
2
3
lim (6 − y)(y + 1) =
lim 3(x2 + 12) =
lim
=
y→−1
x→0
s→8
s + 12
Correct Answers:
• 14
84. (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 7.pg
2
Let f (x) = xx2−11x+28
.
+3x−28
Calculate lim f (x) by first finding a continuous function which
Correct Answers:
•
•
•
•
•
•
x→4
is equal to f everywhere except x = 4.
lim f (x) =
x→4
Correct Answers:
• -0.272727272727273
14
32
-9
56
56
6
0.5
89. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 4.pg
Evaluate the limit
lim 4(3x + 4)3
Note: you can click on the graph to get a larger image.
x→3
Determine the limits for the function f at x = 1.
Note: limits are all integers (e.g. · · · , −2, −1, 0, 1, 2, · · ·).
Correct Answers:
• 8788
lim f (x) =
x→1−
f (1) =
90. (1 pt)
Library/Rochester/setLimitsRates2Limits/ur lr 2 5.pg
√
 −1 − x + 3, if x < −2

Let f (x) = 3,
if x = −2


2x + 8,
if x > −2
Calculate the following limits. Enter DNE for a limit which
does not exist.
lim f (x) =
lim f (x) =
x→1+
Is this function continuous at x = 1?:
Can one change the value of this function at x = 1 to some value
other than its current value at x = 1, and have the function be
continuous at x = 1?:
x→−2−
lim f (x) =
Correct Answers:
x→−2+
•
•
•
•
•
lim f (x) =
x→−2
Correct Answers:
• 4
• 4
• 4
2
-3
-1
no
No
93. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 5 mo.pg
Evaluate the limit
x−5
lim
x→−3 6x2 − 4x + 8
91. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 12.pg
Evaluate the limit
5(y2 − 1)
lim 2
y→4 7y (y − 1)3
Correct Answers:
• -0.108108
Correct Answers:
• 0.0248015873015873
94. (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 4.pg
(
6 − x − x2 , if x ≤ 2
Let f (x) =
2x − 5,
if x > 2
Calculate the following limits. Enter 1000 if the limit does not
exist.
lim f (x) =
lim f (x) =
lim f (x) =
92. (1 pt) Library/Rochester/setLimitsRates2Limits/ns2 2 6.pg
Let f be the function below.
x→2−
x→2+
x→2
Correct Answers:
• 0
• -1
• 1000
95. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 3 mo.pg
Evaluate the limit
lim 7x2 + 8 (5x + 8)
x→5
Correct Answers:
• 6039
15
96. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 48.pg
Evaluate the limit
|x + 15|
lim
−
x→−15 x + 15
100. (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 8.pg
4x+8
Let f (x) = x2 −5x−14
.
Calculate lim f (x) by first finding a continuous function which
x→−2
is equal to f everywhere except x = −2.
lim f (x) =
Correct Answers:
• -1
x→−2
Correct Answers:
97. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 16.pg
Evaluate the limit
x2 + 13x + 42
lim
x→−7
x+7
• -0.444444444444444
101. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 19.pg
Evaluate the limit
t3 − t
t→1 t 2 − 1
lim
Correct Answers:
• -1
98. (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 10b.pg
a
-1
lim f (x) DNE
0
3
1
3
2
3
3
0
4
3
lim f (x)
0
3
3
3
0
DNE
f (a)
lim g(x)
0
DNE
3
0
2
0
3
3
0
3
3
1
lim g(x)
2
0
3
3
3
DNE
g(a)
2
0
3
3
3
1
x→a−
x→a+
x→a−
x→a+
Correct Answers:
• 1
102. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 5.pg
Evaluate the limit
lim
x→−3
Using the table above calcuate the limits below.
Enter ’DNE’ if the limit doesn’t exist OR if limit can’t be determined from the information given.
1. f (1)g(1)
2. lim [ f (g(x))]
x−6
6x2 − 6x + 5
Correct Answers:
• -0.116883116883117
103. (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 11.pg
x→1−
If
3. lim [ f (x)/g(x)]
x→1−
9x − 29 ≤ f (x) ≤ x2 + 3x − 20
4. f (1)/g(1)
determine lim f (x) =
x→3
What theorem did you use to arrive at your answer?
Correct Answers:
• 6
• 3
• DNE
• 0.667
Correct Answers:
• -2
• The Squeeze theorem
99. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 18.pg
Evaluate the limit
x−3
lim
x→3 x2 + 6x − 27
104. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 2 23.pg
The slope of the tangent line to the graph of the function y = 3x3
3 −24
at the point (2, 24) is limx7→2 3xx−2
. By trying values of x near
2, find the slope of the tangent line.
Correct Answers:
Correct Answers:
• 0.0833333333333333
• 36
16
Correct Answers:
• 27
• 0.166666666666667
105. (1 pt) Library/Rochester/setLimitsRates6Rates/s1
√ 6 3.pg
The slope of the tangent line to the curve y = 2 x at the point
(6, 4.8990) is:
The equation of this tangent line can be written in the form
y = mx + b where m is:
and where b is:
109. (1 pt) Library/Rochester/setLimitsRates5Continuity/ur lr 5 5.pg
A function f (x) is said to have a jump discontinuity at x = a if:
1. lim f (x) exists.
x→a−
Correct Answers:
• 0.408248290463863
• 0.408248290463863
• 2.44948974278318
2. lim f (x) exists.
x→a+
3. The left and right limits are not equal.

2

x + 5x + 6, if x < 8
Let f (x) = 25,
if x = 8


−3x + 2,
if x > 8
Show that f (x) has a jump discontinuity at x = 8 by calculating
the limits from the left and right at x = 8.
lim f (x) =
106. (1 pt) Library/Rochester/setLimitsRates5Continuity/ur lr 5 8.pg
Find c such that the function
2
x − 4,
x≤c
f (x) =
8x − 20, x > c
is continuous everywhere.
c=
x→8−
Correct Answers:
• 4
lim f (x) =
x→8+
Now for fun, try to graph f (x).
107. (1 pt) Library/Rochester/setLimitsRates5Continuity/ur lr 5 1.pg
Correct Answers:
• 110
• -22
A function f (x) is said to have a removable discontinuity
at x = a if:
1. f is either not defined or not continuous at x = a.
2. f (a) could either be defined or redefined so that the new
function IS continuous at x = a.
110. (1 pt) Library/Rochester/setLimitsRates5Continuity/s1 5 37.pg
For what value of the constant c is the function f continuous on
(−∞, ∞) where
(
ct + 2
if t ∈ (−∞, 2]
f (t) =
2
ct − 2 if t ∈ (2, ∞)
2
Let f (x) = 2x +3x−44
x−4
Show that f (x) has a removable discontinuity at x = 4 and determine what value for f (4) would make f (x) continuous at
x = 4.
Must define f (4) =
.
Correct Answers:
• 2
Correct Answers:
• 19
111. (1 pt) Library/Michigan/Chap1Sec7/Q17.pg
Find k so that the following function is continuous on any interval:
108. (1 pt) Library/Rochester/setLimitsRates5Continuity/ur lr 5 4.pg
A function f (x) is said to have a jump discontinuity at x = a if:
1. lim f (x) exists.
f (x) = kx
x→a−
if 0 ≤ x < 1,
2. lim f (x) exists.
k=
3. The left and right limits are not equal.
Correct Answers:
• 7*1
x→a+
and
f (x) = 7x2
if
1 ≤ x.
112. (1 pt) Library/Michigan/Chap1Sec7/Q19.pg
If possible, choose k so that the following function is continuous
on any interval:
( 5
6x −12x4
x 6= 2
x−2
f (x) =
k
x = 2.
(
4x − 1, if x < 7
Let f (x) =
2
if x ≥ 7
x+5 ,
Show that f (x) has a jump discontinuity at x = 7 by calculating
the limits from the left and right at x = 7.
lim f (x) =
x→7−
k=
(If no k will make the function continuous, enter none)
lim f (x) =
x→7+
Now for fun, try to graph f (x).
Correct Answers:
17
• 6*(2)ˆ4
115. (1 pt) Library/Union/setLimitConcepts/ur lr 1-5 1.pg
Let F be the function whose graph is shown below. Evaluate
each of the following expressions.
(If a limit does not exist or is undefined, enter “DNE”.)
113. (1 pt) Library/Michigan/Chap1Sec8/Q21.pg
For the function
 2
x − 4, 0 ≤ x < 3



0,
x=3
f (x) =

2x − 1,



3<x
1.
2.
3.
4.
5.
use algebra to find each of the following limits:
lim f (x) =
x→3+
6.
lim f (x) =
x→3−
7.
lim f (x) =
x→3
8.
(For each, enter dne if the limit does not exist.)
Sketch a graph of f (x) to confirm your answers.
lim F(x) =
x→−1−
lim F(x) =
x→−1+
lim F(x) =
x→−1
F(−1) =
lim F(x) =
x→1−
lim F(x) =
x→1+
lim F(x) =
x→1
lim F(x) =
x→3
9.
F(3) =
Correct Answers:
• 2*3 + -1
• 3*3 - 4
• 3*3 - 4
114. (1 pt) Library/Union/setLimitInfinity/ns2 2 xxx.pg
Evaluate the following limits:
2
=
1.
lim
x→5− (x − 5)3
1
2.
lim
=
x→0 x2 (x + 7)
2
3.
lim
=
x→3+ x − 3
1
4.
lim
=
x→−7− x2 (x + 7)
The graph of y = F(x).
Correct Answers:
• 2
• 2
• 2
• 3
• 3
• 4
• DNE
• 1
• DNE
Correct Answers:
•
•
•
•
-infinity
infinity
infinity
-infinity
c
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