Name: ________________________ Class: ___________________ Date: __________
ID: A
Test # 1 Review
Short Answer
1. Find all intercepts:
10. Write an equation of the line that passes through
the given point and is perpendicular to the given
line.
y  64x  x 3
2. Find all intercepts:
y  (x  5 )
4x
2
Point
Line
ÊÁ 1, 7 ˆ˜
Ë
¯
x6
11. Write an equation of the line that passes through
the given point and is parallel to the given line.
3. Test for symmetry with respect to each axis and to
the origin.
x2  2
y
x
4. Find the points of intersection of the graphs of the
equations:
Point
Line
ÊÁ 3, 4 ˆ˜
Ë
¯
2x  5y  9
12. Find an equation of the line through the points of
intersection of y  x 2 and y  6x  x 2 .
x  y2  3
13. Write an equation of the line that passes
through the point ÊÁË 6,4 ˆ˜¯ and is perpendicular
y  x1
to the line x  y  5.
5. Find the slope of the line passing through the points
ÊÁ 1 8 ˆ˜
Ê
ˆ
ÁÁ  , ˜˜ and ÁÁÁ  3 , 1 ˜˜˜ .
ÁÁ 8 3 ˜˜
ÁÁ 16 24 ˜˜
Ë
¯
Ë
¯
14. Evaluate (if possible) the function f(x) 
x  9 . Simplify the result.
6. Find the y-intercept of the line x  4y  8 .
x  5 at
15. Let f (x )  14x  8 . Then simplify the expression
f(x)  f(9)
.
x9
7. Find an equation of the line that passes through the
point (7, 2) and has the slope m that is undefined.
16. Find the domain and range of the function
g(t)  t  10 .
8. Find an equation of the line that passes through the
points (18,  7) and (18, 23).
17. Find the domain and range of the function
11
h(x) 
.
x6
9. Use the result, “the line with intercepts
x y
ÁÊ a,0 ˜ˆ and ÁÊ 0,b ˜ˆ has the equation   1,
Ë ¯
Ë ¯
a b
a  0, b  0”, to write an equation of the line
with x-intercept: ÊÁË 8,0ˆ˜¯ and y-intercept: ÊÁË 0,7ˆ˜¯ .
18. Determine whether y is a function of x.
y  5x 2  6
1
Name: ________________________
19. Given f(x)  cos x and g(x) 
ID: A

2
21. 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.
x , evaluate
f(g(2)) .
20. Determine whether the function is even, odd, or
neither.
f(x)  x 2 (3  x) 2
22. Complete the table and use the result to estimate the limit.
lim
x3
x3
x  16x  39
2
x
f(x)
2.9
2.99
2.999
3.001
2
3.01
3.1
Name: ________________________
ID: A
28. Let f(x)  3  2x 2 and g (x ) 
limit.
23. Determine the following limit. (Hint: Use the graph
to calculate the limit.)
Ê
ˆ
lim ÁÁÁÁ x 2  4 ˜˜˜˜
¯
x1Ë
x  3 . Find the
lim g ÊÁË f (x ) ˆ˜¯
x2
29. Find the lmit.
ÊÁ x ˆ˜
lim tan ÁÁÁ ˜˜˜˜
ÁË 3 ¯
x
30. Find the limit.
lim cos
x2
x
3
31. Suppose that lim f (x )  11 and lim g (x )  3.
xc
xc
Find the following limit.
24. Find the limit.
È
˘
lim ÍÍÍÎ f (x )  g (x ) ˙˙˙˚
xc
lim 9x 2  36x
x  4
32. Suppose that lim f (x )  15 and lim g (x )  10.
xc
25. Find the limit.
Find the following limit.
lim
x6
x
x 8
lim
2
xc
ÍÈÍ f (x )g (x ) ˙˘˙
ÍÎ
˙˚
26. Find the limit.
33. Find the limit (if it exists).
lim
x4
x5
x1
lim
x  8
27. Let f (x )  4x  2 and g (x )  x 3 . Find the limit.
x8
x 2  64
34. Find the limit (if it exists).
lim g ÊÁË f (x ) ˆ˜¯
x1
lim
x5
3
x4 3
x5
xc
Name: ________________________
ID: A
35. Determine the limit (if it exists).
lim
39. Find the limit (if it exists).
12(1  cos x)
x
x0
lim
2
x  11
x0
sin 4 x
x3
37. Find lim
x  0
lim
x  36
f (x  x )  f (x )
where f (x )  4x  3 .
x
x3

È ˘
lim ÊÁÁ 3 ÍÍÍÎ x  ˙˙˙˚  8 ˆ˜˜
Ë
¯

x  6
È ˘
42. Find the limit (if it exists). Note that f(x)  ÍÍÍÎ x  ˙˙˙˚
represents the greatest integer function.
(ii) lim f(x) (iii) lim f(x)
x3


x 6
x  36
È ˘
41. Find the limit (if it exists). Note that f(x)  ÍÍÍÎ x  ˙˙˚˙
represents the greatest integer function.
38. Use the graph as shown to determine the following
limits, and discuss the continuity of the function at
x  3.
(i) lim f(x)
11  x
x 2  121
40. Find the limit (if it exists).
36. Determine the limit (if it exists).
lim

x3
È ˘
lim ÊÁÁ 2x  ÍÍÍÎ x  ˙˙˙˚ ˆ˜˜
¯
 Ë
x5
43. Find the x-values (if any) at which the function
f (x )  13x 2  15x  15 is not continuous. Which of
the discontinuities are removable?
44. Find the x-values (if any) at which f (x ) 
x  3 
is not continuous.
x3
4
Name: ________________________
ID: A
45. Find the constant a such that the function
ÏÔ
ÔÔ 6,
ÔÔ
f (x )  ÌÔ ax  b,
ÔÔ
ÔÔ 6,
Ó
x  5
5  x  1
x1
is continuous on the entire real line.
46. Find all the vertical asymptotes (if any) of the
5
.
graph of the function f (x ) 
2
(x  3 )
47. Find all the vertical asymptotes (if any) of the
graph of the function f(x) 
48.
x3  8
.
x2
Find the limit.
ÊÁ
1 ˆ˜
lim ÁÁÁÁ x 2  ˜˜˜˜
x¯
x  0 Ë
49. Use a graphing utility to graph the function
f (x ) 
limit
x 2  2x  4
x3  8
lim f (x ) .
x  2
and determine the one-sided

5
ID: A
Test # 1 Review
Answer Section
SHORT ANSWER
1. ANS:
x-intercepts: (0, 0), (–8, 0), (8, 0); y-intercept: (0, 0)
PTS: 1
DIF: Easy
REF: 0.1.22
MSC: Skill
NOT: Section 0.1
2. ANS:
x-intercepts: (–5, 0), (–2, 0), (2, 0); y-intercept: (0, 10)
OBJ: Calculate the intercepts of an equation
PTS: 1
DIF: Easy
MSC: Skill
NOT: Section 0.1
3. ANS:
symmetric with respect to the origin
OBJ: Calculate the intercepts of an equation
REF: 0.1.24
PTS: 1
DIF: Easy
REF: 0.1.37
OBJ: Identify the type of symmetry of the graph of an equation
MSC: Skill
NOT: Section 0.1
4. ANS:
ÊÁ 2,  1 ˆ˜ , ÊÁ 1, 2 ˆ˜
Ë
¯ Ë
¯
PTS: 1
DIF: Medium
REF: 0.1.66
OBJ: Calculate the points of intersection of the graphs of equations
MSC: Skill
NOT: Section 0.1
5. ANS:
42
PTS: 1
DIF: Medium
REF: 0.2.13
OBJ: Calculate the slope of a line passing through two points
NOT: Section 0.2
6. ANS:
(0, 2)
PTS: 1
DIF: Medium
REF: 0.2.25
OBJ: Manipulate a linear equation to determine its y-intercept
NOT: Section 0.2
7. ANS:
x7
MSC: Skill
MSC: Skill
PTS: 1
DIF: Easy
REF: 0.2.30
OBJ: Write an equation of a line given a point on the line and its slope
MSC: Skill
NOT: Section 0.2
1
ID: A
8. ANS:
5
y   x8
6
PTS: 1
DIF: Easy
REF: 0.2.40
OBJ: Write an equation of a line given two points on the line
NOT: Section 0.2
9. ANS:
7x  8y  56  0
PTS: 1
DIF: Easy
REF: 0.2.47
OBJ: Write an equation of a line given its x- and y-intercepts
NOT: Section 0.2
10. ANS:
y  1
MSC: Skill
MSC: Skill
PTS: 1
DIF: Medium
REF: 0.2.61
OBJ: Write an equation of a line given a point on the line and a line to which it is parallel/perpendicular
MSC: Skill
NOT: Section 0.2
11. ANS:
2x  5y  14
PTS: 1
DIF: Medium
REF: 0.2.63
OBJ: Write an equation of a line given a point on the line and a line to which it is parallel/perpendicular
MSC: Skill
NOT: Section 0.2
12. ANS:
y  3x
PTS: 1
DIF: Medium
REF: 0.2.71
OBJ: Write an equation of a line through the points of intersection of quadratic equations
MSC: Skill
NOT: Section 0.2
13. ANS:
x  y  10  0
PTS: 1
DIF: Medium
REF: 0.2.64b
OBJ: Write an equation of a line given a point on the line and a line to which it is perpendicular
MSC: Skill
NOT: Section 0.2
14. ANS:
2
PTS: 1
MSC: Skill
15. ANS:
14
DIF: Easy
NOT: Section 0.3
REF: 0.3.4a
OBJ: Evaluate a function and simplify
PTS: 1
MSC: Skill
DIF: Medium
NOT: Section 0.3
REF: 0.3.10
OBJ: Simplify a difference quotient
2
ID: A
16. ANS:
none of the above
PTS: 1
DIF: Easy
REF: 0.3.16
OBJ: Identify the domain and range of a function
NOT: Section 0.3
17. ANS:
domain: (,  6)  (6, )
range: (, 0)  (0, )
PTS: 1
DIF: Easy
REF: 0.3.20
OBJ: Identify the domain and range of a function
NOT: Section 0.3
18. ANS:
yes
MSC: Skill
MSC: Skill
PTS: 1
MSC: Skill
19. ANS:
1
DIF: Easy
NOT: Section 0.3
REF: 0.3.46
OBJ: Identify equations that are functions
PTS: 1
MSC: Skill
20. ANS:
neither
DIF: Easy
NOT: Section 0.3
REF: 0.3.60a
OBJ: Evaluate composite functions
PTS: 1
DIF: Easy
REF: 0.3.69
OBJ: Identify the type of symmetry of the graph of a function
NOT: Section 0.3
21. ANS:
V  x(22  2x) 2
MSC: Skill
PTS: 1
MSC: Application
22. ANS:
–0.100000
DIF: Medium
NOT: Section 0.3
REF: 0.3.97a
OBJ: Create functions in applications
PTS: 1
MSC: Skill
23. ANS:
5
DIF: Medium
NOT: Section 1.2
REF: 1.2.1
OBJ: Estimate a limit from a table of values
PTS: 1
DIF: Medium
REF: 1.2.16
OBJ: Estimate the limit of a function from its graph
NOT: Section 1.2
3
MSC: Skill
ID: A
24. ANS:
0
PTS: 1
MSC: Skill
25. ANS:
3
22
DIF: Easy
NOT: Section 1.3
REF: 1.3.9
OBJ: Evaluate a limit using properties of limits
PTS: 1
MSC: Skill
26. ANS:
1
DIF: Easy
NOT: Section 1.3
REF: 1.3.19
OBJ: Evaluate a limit using properties of limits
PTS: 1
MSC: Skill
27. ANS:
8
DIF: Medium
NOT: Section 1.3
REF: 1.3.22
OBJ: Evaluate a limit using properties of limits
PTS: 1
MSC: Skill
28. ANS:
14
DIF: Medium
NOT: Section 1.3
REF: 1.3.24c
OBJ: Evaluate the limit of composite functions
PTS: 1
MSC: Skill
29. ANS:
3
DIF: Medium
NOT: Section 1.3
REF: 1.3.25c
OBJ: Evaluate the limit of composite functions
PTS: 1
MSC: Skill
30. ANS:
1

2
DIF: Medium
NOT: Section 1.3
REF: 1.3.28
OBJ: Evaluate the limit of the function
PTS: 1
MSC: Skill
31. ANS:
–8
DIF: Easy
NOT: Section 1.3
REF: 1.3.29
OBJ: Evaluate a limit using properties of limits
PTS: 1
DIF: Medium
REF: 1.3.37b
OBJ: Evaluate the limit of a function using properties of limits
NOT: Section 1.3
32. ANS:
150
PTS: 1
DIF: Medium
REF: 1.3.37c
OBJ: Evaluate the limit of a function using properties of limits
NOT: Section 1.3
4
MSC: Skill
MSC: Skill
ID: A
33. ANS:
1

16
PTS: 1
DIF: Medium
REF: 1.3.51
OBJ: Evaluate the limit of a function analytically
NOT: Section 1.3
34. ANS:
1
6
PTS: 1
DIF: Medium
REF: 1.3.55
OBJ: Evaluate the limit of a function analytically
NOT: Section 1.3
35. ANS:
6
PTS: 1
DIF: Medium
REF: 1.3.66
OBJ: Evaluate the limit of a function analytically
NOT: Section 1.3
36. ANS:
0
PTS: 1
DIF: Medium
REF: 1.3.69
OBJ: Evaluate the limit of a function analytically
NOT: Section 1.3
37. ANS:
4
PTS:
OBJ:
NOT:
38. ANS:
1 ,1 ,1
1
DIF: Medium
REF: 1.3.85
Evaluate the limit of a difference quotient
Section 1.3
MSC: Skill
MSC: Skill
MSC: Skill
MSC: Skill
MSC: Skill
, not continuous
PTS: 1
DIF: Medium
REF: 1.4.3a
OBJ: Estimate a limit and points of discontinuity from a graph
NOT: Section 1.4
39. ANS:
1

22
PTS: 1
MSC: Skill
DIF: Easy
NOT: Section 1.4
REF: 1.4.10
5
MSC: Skill
OBJ: Evaluate one-sided limits
ID: A
40. ANS:
1
12
PTS: 1
MSC: Skill
41. ANS:
13
DIF: Medium
NOT: Section 1.4
REF: 1.4.12
OBJ: Evaluate one-sided limits
PTS: 1
MSC: Skill
42. ANS:
5
DIF: Medium
NOT: Section 1.4
REF: 1.4.23
OBJ: Evaluate one-sided limits
PTS: 1
DIF: Medium
MSC: Skill
NOT: Section 1.4
43. ANS:
continuous everywhere
REF: 1.4.24
OBJ: Evaluate one-sided limits
PTS: 1
DIF: Medium
REF: 1.4.38
OBJ: Identify the removable discontinuities of a function
MSC: Skill
NOT: Section 1.4
44. ANS:
f (x ) is not continuous at x  3 and the discontinuity is nonremovable.
PTS: 1
DIF: Medium
REF: 1.4.49
OBJ: Identify the removable discontinuities of a function
NOT: Section 1.4
45. ANS:
a  2 , b  4
MSC: Skill
PTS: 1
DIF: Medium
REF: 1.4.67
OBJ: Identify the value of a parameter to ensure a function is continuous
MSC: Skill
NOT: Section 1.4
46. ANS:
x3
PTS: 1
DIF: Easy
REF: 1.5.14
OBJ: Identify the vertical asymptotes (if any) of the graph of a function
MSC: Skill
NOT: Section 1.5
47. ANS:
no vertical asymptotes
PTS: 1
DIF: Medium
REF: 1.5.25
OBJ: Identify the vertical asymptotes (if any) of the graph of a function
MSC: Skill
NOT: Section 1.5
6
ID: A
48. ANS:

PTS: 1
MSC: Skill
49. ANS:

DIF: Medium
NOT: Section 1.5
REF: 1.5.48
OBJ: Evaluate one-sided limits
PTS: 1
MSC: Skill
DIF: Medium
NOT: Section 1.5
REF: 1.5.55
OBJ: Estimate one-sided limits from a graph
7