Name: ________________________ Class: ___________________ Date: __________
Review Sheet - Math 181
1. Find all intercepts:
y  x 2  2x  63
a.
b.
c.
d.
e.
x-intercept: (9, 0); y-intercept: (0, –63)
x-intercepts: (7, 0), (9,0); y-intercepts: (0, –63), (0, 63)
x-intercepts: (–7, 0), (9,0); y-intercept: (0, 63)
x-intercept: (63, 0); y-intercepts: (0, 7), (0, 9)
x-intercepts: (7,0), (9,0); y-intercepts: (0, 7), (0, 9)
2. Find all intercepts:
y  (x  5 )
a.
b.
c.
d.
e.
4  x2
x-intercepts: (–5, 0), (–2, 0), (2, 0); y-intercepts: (0, 0), (0, 10)
x-intercepts: (–5, 0), (2, 0); y-intercept: (0, 10)
x-intercepts: (–5, 0), (2, 0); y-intercept: (0, –10)
x-intercepts: (–5, 0), (–2, 0), (2, 0); y-intercept: (0, 10)
x-intercepts: (–5, 0), (–2, 0), (2, 0); y-intercept: (0, –10)
3. Test for symmetry with respect to each axis and to the origin.
x2y2  8
a.
b.
c.
d.
e.
symmetric with respect to the origin
symmetric with respect to the x-axis
symmetric with respect to the y-axis
no symmetry
A, B, and C
4. Test for symmetry with respect to each axis and to the origin.
y
x2  2
x
a.
b.
c.
d.
e.
symmetric with respect to the origin
symmetric with respect to the y-axis
symmetric with respect to the x-axis
both B and C
no symmetry
2
ID: A
Name: ________________________
ID: A
5. Which of the following is the correct graph of y  
a.
d.
b.
e.
2  x2 ?
c.
2
Name: ________________________
ID: A
6. Sketch the graph of the equation:
x  4  y2
a.
d.
b.
e.
c.
3
Name: ________________________
ID: A
7. Sketch the graph of the equation:
y  x  2 
a.
d.
b.
e.
none of the above
c.
4
Name: ________________________
ID: A
8. Sketch the graph of the equation:
y  x 3  3x
a.
d.
b.
e.
none of the above
c.
5
Name: ________________________
ID: A
9. The resistance y in ohms of 1000 feet of solid metal wire at 77F can be approximated by the model
12,000
y
 0.46, 5  x  100, where x is the diameter of the wire in mils (0.001 in). If the diameter of the wire is
x2
doubled, the resistance is changed by approximately what factor? In determining your answer, you can ignore the
constant –0.46.
a.
b.
c.
d.
e.
1
2
1
5
4
5
1
4
10. Estimate the slope of the line from the graph.
a.
3
b.

c.
d.
e.
1
3
1

6
1
6
6
6
Name: ________________________
ID: A
11. Find the slope of the line passing through the pair of points.
ÊÁ 3, 6 ˆ˜ , ÊÁ 0, 11 ˆ˜
Ë
¯ Ë
¯
a.
b.
c.
d.
e.
3
5
5

3
5
3
0
3

5
ÁÊ 1 8 ˜ˆ
ÁÊ 3
1 ˜ˆ˜˜
12. Find the slope of the line passing through the points ÁÁÁÁ  , ˜˜˜˜ and ÁÁÁÁ  ,
˜˜ .
Ë 8 3¯
Ë 16 24 ¯
a.
b.
c.
d.
e.
63
21
42
21
42
3
13. Sketch the line passing through the point (3, 4) with the slope  .
2
7
Name: ________________________
ID: A
14. A moving conveyor is built to rise 1 meter for every 5 meters of horizontal change. Suppose the conveyor runs
between two floors in a factory. Find the length of the conveyor if the vertical distance between floors is 10 meters.
Round your answer to the nearest meter.
a.
b.
c.
d.
e.
61 meters
39 meters
51 meters
50 meters
41 meters
15. Find the slope of the line x  3y  15.
a.
1
3
b.

c.
1
5
d.

e.
1
5
1
15
1

3
16. Find the y-intercept of the line x  4y  8 .
a.
b.
c.
d.
e.
(0, 2)
(0, 4)
(0, 8)
(4, 0)
(2, 0)
17. Find an equation of the line that passes through the point (7, 2) and has the slope m that is undefined.
a.
b.
c.
d.
e.
y7
x7
y2
x2
y  7x
8
Name: ________________________
ID: A
9
18. Find an equation of the line that passes through the point (11,  9) and has the slope m  .
2
a.
b.
c.
d.
e.
9
81
x–
2
2
9
81
y x+
2
2
9
y  x + 162
2
9
y x
2
9
y x
2
y
19. Find an equation of the line that passes through the points (18,  7) and (18, 23).
a.
b.
c.
d.
e.
5
y   x8
6
5
y  x8
6
5
y  x8
6
5
y   x8
6
5
y x
6
20. Sketch a graph of the equation y  8  2 (x  4 ) .
9
Name: ________________________
ID: A
21. Write an equation of the line that passes through the given point and is parallel to the given line.
Point
Line
ÊÁ 3, 4 ˆ˜
Ë
¯
2x  5y  9
a.
b.
c.
d.
e.
2x  5y  14
2x  5y  23
2x  5y  14
2x  5y  26
2x  5y  23
22. Write an equation of the line that passes through the point ÊÁË 6,4 ˜ˆ¯ and is perpendicular to the line
x  y  5.
a.
b.
c.
d.
e.
x  y  10  0
xy2 0
xy2 0
x  y  10  0
xy5 0
23. A company reimburses its sales representatives $ 175 per day for lodging and meals plus 45¢ per mile driven. Write
a linear equation giving the daily cost C to the company in terms of x , the number of miles driven. Round the
numerical values in your answer to two decimal places, where applicable.
a.
b.
c.
d.
e.
C  1.75x  45
C  0.45x  175
C  0.45x  175
C  0.45x  175
C  1.75x  45
24. A company reimburses its sales representatives $ 160 per day for lodging and meals plus 42¢ per mile driven. How
much does it cost the company if a sales representative drives 135 miles on a given day? Round your answer to the
nearest cent.
a.
b.
c.
d.
e.
227.20
216.70
136.35
161.35
191.70
25. Evaluate (if possible) the function f(x)  6x  5 at x  2 . Simplify the result.
a.
b.
c.
d.
e.
–7
17
3
7
undefined
10
Name: ________________________
26. Evaluate (if possible) the function f(x) 
a.
b.
c.
d.
e.
ID: A
x  5 at x  9 . Simplify the result.
3
2
2
4
undefined
27. Evaluate (if possible) the function g(x)  x 2 (x  2) at x  t  6 . Simplify the result.
a.
b.
c.
d.
e.
t 3  4t 2  12t  144
t 3  4t 2  84t  144
t 3  16t 2  84t  144
t 3  16t 2  12t  144
none of the above
28. Let f (x )  14x  8 . Then simplify the expression
a.
b.
c.
d.
e.
15
14
19
11
undefined
29. Let g(x) 
g(x)  g(11)
1
. Evaluate the expression
and then simplify the result.
x  11
x  15
a.
2 x  15  x  15
2(x  11)(x  15)
b.
2 x  15  x  15
2(x  11)(x  15)
c.
2 x  15  x  15
2(x  11)(x  15)
d.
e.
f(x)  f(9)
.
x9
2 x  15  x  15
2(x  11)(x  15)
undefined
11
Name: ________________________
ID: A
30. Find the domain and range of the function f(x)  x 2  6.
a.
b.
c.
d.
e.
domain: [6, )
range: [6, )
domain: [6, )
range: (6, )
domain: (, )
range: (6, )
domain: (, )
range: [6, )
domain: (, )
range: [6, )
31. Find the domain and range of the function g(t) 
a.
b.
c.
d.
e.
domain: [10, )
range: (0, )
domain: (10, )
range: [0, )
domain: [10, )
range: (, )
domain: [0, )
range: [10, )
none of the above
32. Find the domain and range of the function h(x) 
a.
b.
c.
d.
e.
t  10 .
11
.
x6
domain: (,  6)  (6, )
range: (, )
domain: (,  6)  (6, )
range: (, 0)  (0, )
domain: (,  6]  [6, )
range: (, 0)  (0, )
domain: (,  6)
range: (0, )
domain: (6, )
range: (0, )
12
Name: ________________________
ID: A
ÔÏÔ 2x  1, x  0
33. Evaluate the function f(x)  ÔÌ
at f(5) .
ÔÔÔ 2x  2, x  0
Ó
a.
b.
c.
d.
e.
f(5)  6
f(5)  5
f(5)  13
f(5)  11
f(5)  12
ÏÔ
Ô 3x  2, x  0
34. Determine the domain and range of the function f(x)  ÔÌÔ
.
ÔÔÓ 3x  6, x  0
a.
b.
c.
d.
e.
domain: (, 2)
range: (, 2)  [6, ]
domain: (, )
range: (, 2)  [6, )
domain: (, )
range: (, 2)  (, 6]
domain: (, )
range: (, 2)  (6,  )
domain: (, 3)
range: (, 2)  [6, )
35. Determine whether y is a function of x.
xy  x 2  3y  x
a.
b.
no
yes
36. Given f(x)  cos x and g(x) 
a.
b.
c.
d.
e.

2
x , evaluate f(g(2)) .
0
1
2

2
1

2
sin(2)
cos(2)
13
Name: ________________________
ID: A
37. Determine whether the function is even, odd, or neither.
f(x)  x 2 (3  x) 2
a.
b.
c.
odd
even
neither
38. Determine whether the function is even, odd, or neither.
f(x)  x sin 2x
a.
b.
c.
even
odd
neither
ÊÁ 9 ˆ˜
39. Find the coordinates of a second point on the graph of a function f if the given point ÁÁÁÁ  , 5 ˜˜˜˜ is on the graph and
Ë 8 ¯
the function is odd.
a.
b.
c.
d.
e.
ÊÁ
ˆ
ÁÁ 5,  9 ˜˜˜
ÁÁ
8 ˜˜¯
Ë
ÊÁ 9
ˆ
ÁÁ ,  5 ˜˜˜
ÁÁ 8
˜˜
Ë
¯
ÊÁ
ˆ
˜
ÁÁ 5, 9 ˜˜
ÁÁ
8 ˜˜¯
Ë
ÊÁ 9
ˆ
ÁÁ  ,  5 ˜˜˜
ÁÁ 8
˜˜
Ë
¯
ÁÊÁ 9 ˜ˆ˜
ÁÁ , 5 ˜˜
Á8 ˜
Ë
¯
14
Name: ________________________
ID: A
40. An open box of maximum volume is to be made from a square piece of material 22 centimeters on a side by cutting
equal squares from the corners and turning up the sides (see figure). Write the volume V as a function of x, the
length of the corner squares.
a.
b.
c.
d.
e.
V  x(22  2x) 2
V  x  (22  x) 2
V  x 2  (22  2x)
V  x 2 (22  2x)
V  x(22  2x)
41. An open box of maximum volume is to be made from a square piece of material 30 centimeters on a side by cutting
equal squares from the corners and turning up the sides(see figure). What is the domain of the function
V  x(30  2x) 2 .
a.
b.
c.
d.
e.
domain: 0  x  
domain: 30
domain: 0  x  15
domain: 0  x  30
domain: 15
15
Name: ________________________
ID: A
42. Determine which type of function would be most appropriate to fit the given data.
a.
b.
c.
d.
e.
exponential
linear
quadratic
no relationship
trigonometric
43. Which function below would be most appropriate model for the given data?
a.
b.
c.
d.
no apparent relationship between x and y
trigonometric
quadratic
linear
16
Name: ________________________
ID: A
44. The motion of an oscillating weight suspended by a spring was measured by a motion detector. The data collected
and the approximate maximum (positive and negative) displacements from equilibrium are shown in the figure.
The displacement is measured in centimeters, and the time is measured in seconds. Take A(0.133,2.49) and
B(0.343,1.78). Approximate the amplitude and period of the oscillations.
a.
b.
c.
d.
e.
Amplitude = 0.335. Period = 4.3.
Amplitude = 0.71. Period = 2.1.
Amplitude = 0.355. Period = 4.2.
Amplitude = 4.2. Period = 0.355.
Amplitude = 2.1. Period = 0.71.
17
ID: A
Review Sheet - Math 181
Answer Section
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
D
E
A
B
B
D
D
E
E
B
C
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
Easy
Easy
Easy
Easy
Easy
Easy
Medium
Easy
Medium
Easy
Easy
Medium
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Application
Skill
Skill
Skill
14.
15.
16.
17.
18.
19.
DIF:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
Easy
C
E
A
B
B
D
MSC:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
Skill
Medium
Medium
Medium
Easy
Easy
Easy
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
Application
Skill
Skill
Skill
Skill
Skill
1
ID: A
20. ANS:
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
DIF:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
Medium
A
A
B
B
D
B
C
B
A
E
E
B
E
B
B
D
C
A
B
A
C
A
D
C
MSC:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
Skill
Medium
Medium
Easy
Easy
Easy
Easy
Easy
Medium
Medium
Easy
Easy
Easy
Easy
Easy
Easy
Easy
Easy
Easy
Easy
Medium
Medium
Easy
Easy
Easy
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
Skill
Skill
Application
Application
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Skill
Application
Application
Skill
Skill
Application
2