Practice test Ch 2
Math 245
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the center-radius form of the equation of the circle.
1) center (0, 0), radius 5
1)
Graph the circle.
2) (x - 5)2 + (y + 4)2 = 9
2)
Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
3) x2 + y2 + 14x + 2y + 1 = 0
3)
Use the graph to determine the equation of the circle in center-radius form.
4)
4)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the equation with the correct graph.
5) 7x + 6y = -18
A)
C)
B)
D)
5)
6) y =
1
x+1
5
6)
A)
B)
C)
D)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Graph the function.
7) f(x) = 2x2
7)
Find the specified domain.
8) Find the domain of (f - g)(x) when f(x) = 9x - 5 and g(x) = 5x - 4.
8)
For the given functions f and g , find the indicated composition.
9) f(x) = x + 4, g(x) = 8x - 8
(f g)(x)
9)
Find the requested function value.
10) Find (f
g)(-6) when f(x) = 9x + 2 and g(x) = -9x2 - 2x + 1.
10)
Evaluate.
11) Find (f - g)(1) when f(x) = 3x2 + 3 and g(x) = x + 6.
Solve the problem.
12) Use the tables to find (fg)(-9).
x -9 -3 5
f(x) -5 -4 8
11)
12)
x -9 1 5
g(x) -7 -4 -6
For the pair of functions, find the indicated sum, difference, product, or quotient.
13) f(x) = 2x2 - 5x, g(x) = x2 - 2x - 15
13)
Describe the transformations and give the equation for the graph.
14)
14)
f
Find
(x).
g
Graph the function.
1
-x
15) f(x) =
2
15)
16) y = -3 x
Give the domain and range of the relation.
17) Annual New Telemarketing Companies
Year Number
1993
52
1994
102
1995
187
1996
170
1997
218
Decide whether the relation defines a function.
18) {(-3, -2), (3, 6), (4, 6), (7, -7), (10, -1)}
16)
17)
18)
19)
19)
20)
20)
The graph of y = f(x) is given. Use the graph to find the function value.
21) Find f(-5).
21)
Find the center-radius form of the equation of the circle.
22) center (- 15, -5), radius 15
22)
Evaluate the function.
23) Find g(a + 1) when g(x) =
1
x - 3.
4
23)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the graph to solve the problem.
24) The height h in feet of a projectile thrown upward from the roof of a building after time t seconds is
shown in the graph below. How high will the projectile be after 3.9 s?
A) 250 ft
B) 225 ft
C) 200 ft
D) 275 ft
24)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
25) 5x - 15y = 15
25)
Write an equation for the line described. Write the equation in the form specified.
26) perpendicular to y = 6, through (9, 8)
26)
The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope-intercept form.
27)
27)
Find the average rate of change illustrated in the graph.
28)
Distance
Traveled
(in miles)
Time (in hours)
28)
Solve the problem. Write all linear equations in slope-intercept form.
29) A house was purchased for $79,000. After 5 years the value of the house was $99,000. Find
a linear equation that models the value of the house after x years.
30) The table lists the average annual cost (in dollars) of room and board at public four-year
colleges in the city of Bookhaven for selected years.
29)
30)
PUBLIC FOUR-YEAR COLLEGE ROOM AND BOARD
Year Room and Board (in dollars)
1
1280
2
1565
3
1803
4
2083
5
2395
6
2685
Determine a linear function f defined by f(x) = mx + b that models the data using (1, 1280)
and (6, 2685).
Determine the intervals of the domain over which the function is continuous.
31)
Find the requested value.
32) f(-6) for f(x) = 7x,
x - 1,
if x -1
if x > -1
31)
32)
Graph the function.
2x + 8, if x < 0
33) f(x) =
5x2 - 4 if x 0
34) f(x) = x + 1
Solve the problem.
35) Suppose a car rental company charges $134 for the first day and $84 for each additional or
partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(6.5).
36) The charges for renting a moving van are $50 for the first 30 miles and $9 for each
additional mile. Assume that a fraction of a mile is rounded up. (i) Determine the cost of
driving the van 97 miles. (ii) Find a symbolic representation for a function f that computes
the cost of driving the van x miles, where 0 < x 100. (Hint: express f as a
piecewise-constant function.)
33)
34)
35)
36)
Graph the function.
37) y = x - 5 - 7
38) g(x) =
1
x-6 +4
4
The figure below shows the graph of a function y = f(x). Use this graph to solve the problem.
39) Sketch the graph of y = -f(x).
37)
38)
39)
40) Sketch the graph of y = f(x - 3).
40)
Determine if the function is even, odd, or neither.
41) f(x) = x4 - 5x2 + 3
41)
For the pair of functions, find the indicated sum, difference, product, or quotient.
42) f(x) = 3x - 7, g(x) = 8x - 9
Find (f - g)(x).
Find the specified domain.
43) Find the domain of (f + g)(x) when f(x) = 5x + 7 and g(x) =
3
x - 10
Solve the problem.
44) The graphs of functions f and g are shown. Use these graphs to find (f + g)(-4).
y = f(x)
44)
45)
x -7 4
7
g(x) -1 -9 -4
Compute and simplify the difference quotient
46) f(x) = 9x - 11
43)
y = g(x)
45) Use the tables to find (f + g)(-7).
x -7 1 7
f(x) 1 6 -4
42)
f(x + h) - f(x)
,h
h
0.
46)
Find the requested function value.
47) Find (f
g)(6) when f(x) = -6x - 6 and g(x) = -7x2 - 3x - 3.
For the given functions f and g , find the indicated composition.
g(x) = 3x - 1
48) f(x) = 5x + 13,
(f g)(x)
47)
48)
Answer Key
Testname: M245TEST2PRACTCETEST
1) x2 + y2 = 25
2)
3) yes
4) (x - 4)2 + (y - 2)2 = 16
5) B
6) D
7)
8) (- , )
9) 2 2x - 1
10) -2797
11) -1
12) 35
2x2 - 5x
13)
2
x - 2x - 15
14) It is the graph of f(x) = x translated 5 units to the right and 4 units down. The equation is y = x - 5 - 4
Answer Key
Testname: M245TEST2PRACTCETEST
15)
16)
17) domain: {1993, 1994, 1995, 1996, 1997}; range: {52, 102, 170, 187, 218}
18) Function
19) Not a function
20) Function
21) 5
22) (x + 15)2 + (y + 5)2 = 15
23)
a - 11
4
24) A
25) D = (- , ), R = (- , )
26) x = 9
27) y = -2
Answer Key
Testname: M245TEST2PRACTCETEST
28) 5 miles per hour
29) y = 4000x + 79,000
30) f(x) = 281x + 999
31) (- , 4) (4, )
32) -42
33)
34)
35) $638
36) $653; f(x) =
37)
50
50 + 9(x - 30)
if 0 < x 30
if 30 < x 100
Answer Key
Testname: M245TEST2PRACTCETEST
38)
39)
40)
41) Even
42) -5x + 2
43) (- , 10)
44) 3
45) 0
46) 9
47) 1632
48) 15x + 8
(10, )