Name_______________________________
CID___________
PreCalculus - Chapter 1 Test Prep
Complete every other odd problem for homework, showing work neatly on notebook paper. The remaining problems are
available for extra practice.
Solve the problem.
1) A ball is shot up in the air and its height, h,
above the ground in feet is given by the
function h(x) = - 16x2 + 47x , where x is the
number of seconds the ball has been in flight.
Graph this function and find the x-value for
which the maximum height of the ball is
attained. Round your answer to the
hundredths place.
4) The graph depicts a personʹs speed y, in miles
per hour, during a 15-minute period of
driving.
The graph has two turning points.The first
turning point is the point at which the graph
stops rising and starts to fall. The second
turning point is the point at which the graph
stops falling and starts to rise again.
Estimate and interpret the turning points.
y
100
2) A ball is shot up in the air and its height, h,
above the ground in feet is given by the
function h(x) = - 16x2 + 42x , where x is the
number of seconds the ball has been in flight.
Graph this function and find the maximum
height that the ball attains. Round your
answer to the hundredths place.
75
50
25
5
3) A rock is thrown vertically upward from the
surface of the moon at a velocity of 28 m/sec.
The graph shows the height y of the rock, in
meters, after x seconds. Estimate and interpret
the turning point (the point at which the graph
reaches its maximum value).
y
15 x
10
Solve the equation algebraically.
5) v2 + 5 = 7 - 2v2
1
6) x2 - 7x - = 0
7
400
300
7) (x - 12)2 = 49
200
8) (x - 9)2 = 36
100
9) x(x - 2) = 35
10
20
30
40
50
x
10) x - 8x - 16 = 0
Solve the equation graphically.
11) 9x - 1 = x + 3
12) 2x - 3 = x + 2
13) 4x - 3 = 2 - x - 1
Mrs. Cotton - PreCalculus
Page 1
Name___________________________________CID
14) 5x - 9 = 3 - x - 2
Date
21)
y
10
Determine whether the equation defines y as a function
of x.
5
15) y = 2x - 2
-10
16) x = y 2 + 6
-5
5
10 x
5
10 x
-5
17) y = x2 + 1
-10
18) y = -9x2 + 5x - 2
22)
y
Determine whether the graph is the graph of a function.
10
19)
5
y
10
-10
5
-5
-5
-10
-5
5
10 x
-10
-5
-10
Find the domain of the given function.
23) f(x) = 8 - x
20)
y
24) f(x) = x
x - 6
25) f(x) = (x + 5)(x - 5)
x2 + 25
26) f(x) = x + 9
(x + 5)(x - 6)
10
5
-10
-5
5
-5
10 x
-10
27) f(x) = 28) f(x) = x
x2 + 3x
9 - x2
x - 1
Find the range of the function.
29) f(x) = (x - 1)2 + 1
Mrs. Cotton - PreCalculus
Page 2
Name___________________________________CID
30) f(x) = x2 + 2
Date
38) Use the graph of f to estimate the local
maximum and local minimum.
5
31) f(x) = 6x + 14
y
4
32) f(x) = 3
7
12 - x
2
1
Graph the function and determine if it has a point of
discontinuity at x = 0. If there is a discontinuity, tell
whether it is removable or non-removable.
x2 - 2x
33) g(x) = x
-5
-4
-3
-2
-1
1
2
3
4
5 x
-1
-2
-3
-4
-5
2
34) f(x) = x
35) h(x) = 36) f(x) = 39) Estimate graphically the local maximum and
local minimum of f(x) = 4x2 - 2x + 5.
x
x - 1
40) Determine graphically the local maximum and
local minimum of f(x) = -4x2/3 - 3.
x5 + 3x
x
Determine the intervals on which the function is
increasing, decreasing, and constant.
Solve the problem.
37) Use the graph of f to estimate the local
maximum and local minimum.
5
41)
y
10
y
4
3
2
10 x
-10
1
-5
-4
-3
-2
-1
1
2
3
4
5 x
-1
-10
-2
-3
-4
42)
-5
5
4
3
2
1
-5 -4 -3 -2 -1-1
-2
-3
-4
-5
Mrs. Cotton - PreCalculus
y
1 2 3 4 5 x
Page 3
Name___________________________________CID
Identify intervals on which the function is increasing,
decreasing, or constant.
Date
58) g(x) = x + 8
x2 - 6
horizontal asymptotes(s)
43) f(x) = 25(x + 4)2 - 7
59) f(x) = 1.9x horizontal asymptotes(s)
44) f(x) = x3 - x2 + 3
Determine if the function is bounded above, bounded
below, bounded on its domain, or unbounded on its
domain.
45) y = 7 - x2
46) y = 3 - x2
60) g(x) = x2 + 3x - 3
horizontal asymptotes(s)
x - 3
Identify which of the twelve basic functions listed below
fit the description given.
1
y = x, y = x 2 , y = x 3 , y = x , y = , y = e x , y = x, y = ln x, y
x
= sin x, y = cos x, y = int (x), y = 47) y = 8 -x + 6
1
1 + e -x
61) The three functions that are even
48) y = 6x - x3
62) The one function that is decreasing from (0, ∞)
Determine algebraically whether the function is even,
odd, or neither even nor odd.
63) The four functions with local minima
49) f(x) = 2x2 + 1
64) The two functions with infinitely many zeros
50) f(x) = -6x3 + 2x
Graph the piecewise-defined function.
51) f(x) = 5x4 - 8x - 8
65)
3x + 4, if x < 0
52) f(x) = x + y(x) =
11
x
Find the asymptote(s) of the given function.
x - 4
53) f(x) = vertical asymptotes(s)
x2 + 5
3x2 - 2, if x ≥ 0
66)
∣x∣ - 5, if x < 0
f(x) =
-5, if x ≥ 0
54) f(x) = 55) f(x) = x - 1
vertical asymptotes(s)
2
x + 3x
67) h(x) = x3 if x < 0
x if x ≥ 0
x - 4
vertical asymptotes(s)
x2 - 36
68) f(x) = x if x < 0
cos x if x ≥ 0
56) h(x) = (x - 2)(x + 8)
vertical asymptotes(s)
x2 - 9
5x2 + 7
horizontal asymptotes(s)
57) f(x) = 5x2 - 7
Mrs. Cotton - PreCalculus
Perform the requested operation or operations. Find the
domain of each.
69) f(x) = 3x + 3, g(x) = 9x - 4
Find fg.
Page 4
Name___________________________________CID
70) f(x) = 3x + 5, g(x) = 3x2
Find (f + g)(x).
71) f(x) = x - 7; g(x) = cos x
Find f - g.
Date
Find the inverse of the function.
85) f(x) = 6x + 2
86) f(x) = x + 8
87) f(x) = 7x3 - 1
72) f(x) = 6x + 1; g(x) = 4x - 5
Find f/g.
88) f(x) = 6
x - 3
73) f(x) = x2 + 3 ; g(x) = x - 4
Find g(f(x)).
89) f(x) = -3x + 9
5x - 5
74) f(x) = 8x + 10; g(x) = 5x - 1
Find f(g(x)).
90) f(x) = 3 x
- 8
6
Perform the requested operation or operations.
75) f(x) = x + 10; g(x) = 8x - 14
Find f(g(x)).
76) f(x) = 4x 2 + 6x + 8; g(x) = 6x - 7, find g(f(x)).
Find functions f and g so that h(x) = f(g(x)).
1
77) y = 2
x - 7
Find a direct relationship between x and y.
91) x = 3t and y = 7t + 6
92) x = t - 5 and y = t2 - 2t
Graph the inverse of the function plotted, on the same set
of axes. Use a dashed curve for the inverse.
93)
y
10
78) y = ∣6x + 5∣
79) y = 5
4
+ 7
x2
-10
80) y = (2x - 17)6
Find two functions defined implicitly by the given
relation.
-5
5
10
x
-5
-10
81) x2 + y2 = 100
82) x2 - y2 = 9
Find the (x,y) pair for the value of the parameter.
83) x = 5t and y = t2 - 4 for t = 8
84) x = -9t + 5 and y = 13 - t for t =6
Mrs. Cotton - PreCalculus
Page 5
Name___________________________________CID
94)
Date
Determine if the function is one-to-one.
97)
y
10
y
10
5
5
-10
-5
5
10
x
-10
-5
-5
-5
-10
-10
5
10 x
5
10 x
5
10 x
98)
95)
y
y
10
10
5
5
-10
-10
-5
5
10
-5
x
-5
-5
-10
-10
99)
96)
y
10
y
10
5
-10
10
-10
x
-5
-5
-10
-10
Mrs. Cotton - PreCalculus
Page 6
Name___________________________________CID
100)
sketch the graph of y 2 as a dashed line or curve by one or
y
10
more of these: a vertical and/or horizontal shift of the
graph y1 , a vertical stretch or shrink of the graph of y 1 , or
5
-10
-5
Date
Sketch the graph of y 1 as a solid line or curve. Then
a reflection of the graph of y 1 across an axis.
5
10 x
109) y1 = x2 ; y2 = x2 - 2
y
-5
10
-10
5
Confirm that f and g are inverses by showing that f(g(x)) =
x and g(f(x)) = x.
x - 9
101) f(x) = 8x + 9 and g(x) = 8
-10
-5
5
10
x
5
10
x
10
x
-5
-10
102) f(x) = x + 5
and g(x) = 6x - 5
6
110) y1 = ∣x∣; y2 = -2∣x∣
Describe how the graph of y=x 2 can be transformed to the
graph of the given equation.
y
10
103) y = x2 - 9
5
104) y = (x - 20)2 + 4
-10
-5
Describe how to transform the graph of f into the graph of
g.
-5
105) f(x) = x and g(x) = 7 x
-10
106) f(x) = x and g(x) = 0.1x
111) y1 = x2 ; y2 = (x - 2)2 - 6
107) f(x) = x and g(x) = - -x
y
10
108) f(x) = (x + 4)2 and g(x) = -(x - 2)2
5
-10
-5
5
-5
-10
Mrs. Cotton - PreCalculus
Page 7
Name___________________________________CID
112) y1 = 3 x, y2 = 3 x + 2
120) Joe Pearlman received a 3.5% pay decrease.
His salary after the decrease was $31,845.
What was his salary before the decrease?
y
10
Solve the problem.
5
-10
-5
Date
5
10
x
121) How many liters of a 30% alcohol solution
must be mixed with 40 liters of a 90% solution
to get a 80% solution?
-5
-10
Give the equation of the function g whose graph is
described.
113) The graph of f(x) = ∣x∣ is vertically stretched by
a factor of 4.2. This graph is then reflected
across the x-axis. Finally, the graph is shifted
0.74 units downward.
3
114) The graph of f(x) = x is shifted 4.8 units to
the left. This graph is then vertically stretched
by a factor of 5.5. Finally, the graph is reflected
across the x-axis.
115) The graph of f(x) = x2 - 4x + 3 is horizontally
shrunk by a factor of 1/4 .
116) The graph of f(x) = x3 - 3x 2 + 2x + 1 is
reflected across the y-axis .
Write the specified quantity as a function of the specified
variable.
117) One leg of a right triangle is three times as
long as the other. Write the length of the
hypotenuse as a function of the length of the
shorter leg.
118) The height of a right circular cylinder equals
its diameter. Write the volume of the cylinder
as a function of its radius.
Use an equation to solve the problem.
119) When a number is added to its double and its
triple, the sum is 186. Find the three numbers.
Mrs. Cotton - PreCalculus
Page 8
Answer Key
Testname: CHAPTER 1 TEST PREP
1) 1.47
2) 27.56
3) The turning point is at approximately (17.5, 245). This
is the point at which the rock reaches its maximum
height and starts to fall back towards the surface of
the moon.
4) The first turning point is at approximately (6, 60).
This is where the personʹs speed first stops increasing
and starts to decrease. The second turning point is at
approximately (12, 48). This is where the personʹs
speed stops decreasing and starts to increase again.
2
5) ±
3
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
7 1
± 2 2
33)
9
6
3
-9
-6
-3
3
6
-3
-6
-9
Yes; removable
347
7
5; 19
3; 15
-5; 7
4
0.3
2.6
0.4 ; 1.2
1.3 ; 2.3
Yes
No
Yes
Yes
Yes
Yes
No
No
(-∞, 8]
(-∞,6) ∪ (6,∞)
All real numbers
[-9, -5) ∪ (-5, 6) ∪ (6, ∞)
(-∞, -3) ∪ (-3, 0) ∪ (0, ∞)
[-3, 1) ∪ (1, 3]
[1, ∞)
[2, ∞)
(-∞, ∞)
(-∞, 0) ∪ (0, ∞)
y
34)
5
y
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5 x
1
2
3
4
5 x
-1
-2
-3
-4
-5
Yes; non-removable
35)
5
y
4
3
2
1
-5
-4
-3
-2
-1
-1
-2
-3
-4
-5
No
Mrs. Cotton - PreCalculus
Page 9
9 x
Answer Key
Testname: CHAPTER 1 TEST PREP
65)
36)
5
y
y
10
4
3
5
2
1
-10
-5
-4
-3
-2
-1
1
2
3
4
-5
5
10
x
5
10
x
5
10
x
5 x
-1
-5
-2
-3
-10
-4
-5
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
61)
Yes; removable
Local maximum: approx. 1.17; local minimum:
approx. -3.33
Local maximum: approx. 3.66; local minimum:
approx. -2.55
No local maximum; local minimum: 4.75
Local maximum: -3; no local minimum
Increasing on (-∞, -1); Decreasing on (-1, ∞)
Increasing on (-2, 0) and (3, 5); Decreasing on (1, 3);
Constant on (-5, -2)
Increasing: (-4, ∞); decreasing: (-∞, -4)
Increasing: (-∞, 0) and (0.67, ∞); decreasing: (0, 0.67)
Bounded above
Bounded
Bounded below
Unbounded
Even
Odd
Neither
Odd
None
x = 0, x = -3
x = 6, x = -6
x = 3, x = -3
y = 1
y = 0
y = 0
None
y = x2 , y = cos x, y = x
62) y = 66)
y
10
5
-10
-5
-5
-10
67)
y
10
5
-10
-5
-5
-10
1
x
63) y = x2 , y = sin x, y = cos x, y = x
64) y = sin x, y = cos x
Mrs. Cotton - PreCalculus
Page 10
Answer Key
Testname: CHAPTER 1 TEST PREP
93)
68)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
69) ( 3x + 3)( 9x - 4); domain: 4
,∞
9
10
x
5
10
x
5
10
x
94)
y
10
70) 3x + 5 + 3x2 ; domain: (-∞,∞)
71) x - 7 - cos x; domain: [7, ∞)
5
6x + 1
; domain {x|x ≠ }
72) (f/g)(x) = 4
4x - 5
5
73) g(f(x)) = x2 - 1
74) f(g(x)) = 40x + 2
75) f(g(x)) = 2 2x - 1
76) g(f(x)) = 24x2 + 36x + 41
77) f(x) = 1/x, g(x) = x2 - 7
78) f(x) = ∣x∣, g(x) = 6x + 5
79) f(x) = x + 7, g(x) = 4/x2
5
-10
-5
-5
-10
95)
y
80) f(x) = x6 , g(x) = 2x - 17
81) y = 100 - x2 or y = - 100 - x2
82) y = + x2 - 9 or y = - x2 - 9
10
5
83) (40, 60)
84) (-49, 7)
x - 2
85) f-1 (x) = 6
86) f-1 (x) = x2 - 8, x ≥ 0
-10
-5
-5
-10
3 x + 1
87) f-1 (x) = 7
3x + 6
88) f-1 (x) = x
5x + 9
89) f1 (x) = 5x + 3
90) f-1 (x) = 6(x + 8)3
7
91) y = x + 6
3
92) y = x2 + 8x + 15
Mrs. Cotton - PreCalculus
Page 11
Answer Key
Testname: CHAPTER 1 TEST PREP
96)
110)
y
y
10
10
5
10
-10
x
-10
-5
5
10
x
10
x
10
x
-5
-10
-10
Function is its own inverse.
Yes
No
Yes
No
x - 9
+ 9 = x - 9 + 9 = x
101) f(g(x)) = 8
8
111)
97)
98)
99)
100)
g(f(x)) = 8x + 9 - 9 8x
= = x
8
8
102) f(g(x)) = 6x - 5 + 5 6x
= = x
6
6
y
10
-10
x + 5
- 5 = x + 5 - 5 = x
g(f(x)) = 6
6
-10
112)
103) Shift the graph of y = x2 down 9 units.
104) Shift the graph of y = x2 right 20 units and then up 4
units.
105) Vertically stretch the graph of f by a factor of 7.
106) Horizontally stretch the graph of f by a factor of 10.
107) Reflect the graph of f across the y-axis and then
reflect across the x-axis.
108) Shift the graph of f right 6 units and reflect across the
x-axis
109)
y
10
5
-10
-10
10
113) g(x) = -4.2∣x∣ - 0.74
3
114) g(x) = -5.5 x + 4.8
5
-5
5
-5
-10
Mrs. Cotton - PreCalculus
5
-5
y
-10
-5
10
x
115) g(x) = 4x2 - 16 x + 12
116) g(x) = - x3 - 3x 2 - 2x + 1
117) c = a 10
118) V = 2πr3
119) 31, 62, 93
120) $33,000
121) 8 L
Page 12