Practice Test 2- 1314- 2.3-2.7 Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the description with correct symbolic expression. 1)
1) A linear function whose graph has a y-intercept -8 A) x = -8
C) y = -8x + 19
B) f(x) = -7x - 8
D) -8x + 14y = 19
2) A constant function
2)
A) x = -8
C) y = -8x + 6
B) f(x) = -8
D) -8x + 6y = 6
3) A linear equation whose graph has x-intercept -8 and y-intercept 28 A) -28x + 8y = 224
C) f(x) = -8
B) x = 28
3) D) y = 28x + 224
4) A linear function whose graph passes through the origin A) x = 2
B) y = -4x
C) f(x) = 2
4) D) 7x - 5y = 7
5) A line with a positive slope A) y = x13
5) C) x = -2
B) y = -2x + 13
D) -18x + 9y = 13
6) A vertical line
6)
A) x = 7
B) y = 7x + 6
C) 7x - 7y = 6
D) f(x) = -4x + 7
Graph and give the domain and the range. If it is a constant function, identify it as such. 7) h(x) = 6
7) 6
y
4 2 -6
-4
-2
2
4
6 x
-2 -4 -6
1
A) D = {-∞, ∞}, R = {6} constant function 6
-6
-4
B) D = {6}, R = {-∞, ∞} constant function
y
6
4
4
2
2
-2
2
4
6 x
-6
-2
-4
-4
-6
-6
6
-4
-2
-2
C) D = {-∞, ∞}, R = {6} constant function
-6
-4
6
4
4
2
2 2
2
4
6 x
2
4
6 x
D) D = {6}, R = {-∞, ∞} constant function
y
-2
y
4
6 x
-6
-4
-2
-2
-2
-4
-4
-6
-6
y
Graph and give the domain and the range. 8) x = 3
8) 6
y
4 2 -6
-4
-2
2
4
6 x
-2 -4 -6
2
A) D = {3}, R = {-∞, ∞}
B) D = {-∞, ∞}, R = {3}
y
-6
-4
6
6
4
4
2
2
-2
2
6 x
4
-6
-4
-2
-2
-2
-4
-4
-6
-6
C) D = {3}, R = {-∞, ∞}
-4
4
6 x
2
4
6 x
y
6
6
4
4
2
2
-2
2
D) D = {-∞, ∞}, R = {3}
y
-6
y
2
6 x
4
-6
-4
-2
-2
-2
-4
-4
-6
-6
Find the slope of the line satisfying the given conditions. 9) Vertical, through (6, 8)
9)
A) 0
B) Undefined
C) 1
D) -1
Find the average rate of change illustrated in the graph. 10)
10) 80 70 60
Distance Traveled (in miles)
50 40 30 20 10 1
2
3
4
5
Time (in hours) A) 25 miles per hour
B) .2 miles per hour
C) 5 miles per hour
D) 2.5 miles per hour 3
11)
11) 35 30
Value of Car (in thousands of dollars)
25 20 15 10 5
1
2
3
4
5
6
Year A) -$4000.00 per year
B) $3000.00 per year
C) -$3000.00 per year
D) $4000.00 per year
Write the equation of the line. 12) Vertical, through (-2, 2) A) y = -2
12) B) x = -2
C) y = 2
D) x = 2
13) x-intercept 4, y-intercept 4 A) 4x + 4y = -16
13) B) 4x - 4y = 16
C) 4x + 4y = 16
14) Through (7, -7), perpendicular to -3x + 8y = 35 35 8 35 7 B) y = x + A) y = x - 8 3 3 8
15) Through (-2, 3), parallel to 5x - 4y = -6 11 5 A) y = - x - 2 4
D) -4x + 4y = 16 14)
3 3 C) y = - x - 8 8
8 35 D) y = - x + 3 3
15) 4 3 B) y = x + 5 5
5 11 C) y = x + 4 2
1 3 D) y = - x + 2 2
Solve. 16) In a lab experiment 14 grams of acid were produced in 39 minutes and 17 grams in 41 minutes. Let y be the grams produced in x minutes. A) 2y = 3x + 25
B) 2y = 3x + 89
C) y = x + 25
4
D) 2y = 3x - 89
16)
Match the equation with the correct graph. 17) 2x - 9y = 27
17) y
x
A)
B) y
y
10 8 6 4 2
10 8 6 4 2 2 4 6 8 10 x
-10 -8 -6 -4 -2-2 -4 -6 -8 -10
2 4 6 8 10 x
-10 -8 -6 -4 -2-2 -4 -6 -8 -10
C)
D) y
y
10 8 6 4 2 -10 -8 -6 -4 -2-2 -4 -6 -8 -10
10 8 6 4 2 2 4 6 8 10 x
-10 -8 -6 -4 -2-2 -4 -6 -8 -10
2 4 6 8 10 x
Find the slope and the y -intercept of the line. 18) 6x - 9y = -18 3 A) Slope ; y-intercept (0, -2) 2
18) 2 B) Slope ; y-intercept (0, 2) 3 2 D) Slope - ; y-intercept (0, -2) 3
3 C) Slope - ; y-intercept (0, 2) 2
5
Solve. 19) 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.
19)
PUBLIC FOUR-YEAR COLLEGE ROOM AND BOARD Year Room and Board (in dollars) 1991 1340 1992 1685 1993 1974 1994 2314 1995 2695 1996 3045 Letting x = 0 correspond to 1990, determine a linear function f defined by f(x) = mx + b that models the data using (1, 1340) and (6, 3045). A) f(x) = 2781 - 1441x
B) f(x) = 1340
C) f(x) = 341x + 999
D) f(x) = 999x + 341
Determine the intervals of the domain over which each function is continuous. 20)
20) y
(5, 0) x
A) (-∞, 0) ∪ (0, ∞)
B) (-∞, 5) ∪ (5, ∞)
C) (-∞, 5] ∪ [5, ∞)
D) (-∞, ∞) 21)
21) y
x (-1, -4)
A) (-∞, ∞)
B) (-∞, -1) ∪ (-1, ∞)
C) [-4, ∞)
D) [-1, ∞)
6
Refer to the following graphs to determine an appropriate response. Graph A 4
Graph B
y
y 3
4 x
-4
x
4
-3 -4
Graph C
Graph D y
y 3
3
-3
3
x
4
x
-3
22) Which is not the graph of a function? What is its equation? A) Graph D; y = [[x]]
B) Graph A; y = x
C) Graph C; y = x
D) Graph B; x = y2
22)
Find the requested value. 23)
23) 3x + 3, if x ≤ 0 f(8) for f(x) = 3 - 7x, if 0 < x < 7 x, if x ≥ 7 A) 8
B) -53
C) 7
Graph the function.
7
D) 27
24)
24) 1, if x ≥ 1 f(x) = -4 - x, if x < 1 6
y
4 2
-6
-4
-2
2
4
6 x
-2 -4 -6
A)
B) 6
-6
-4
y
6
4
4
2
2
-2
2
4
6 x
-6
-4
-2
-2
-2
-4
-4
-6
-6
C)
y
2
4
6 x
2
4
6 x
D) 6
-6
-4
y
6
4
4
2
2
-2
2
4
6 x
-6
-4
-2
-2
-2
-4
-4
-6
-6
8
y
25) f(x) = x + 1
25) y
x
A)
B) y
y
x
x
C)
D) y
y
x
x
9
26) f(x) = x - 1
26) y
x
A)
B) y
y
x
x
C)
D) y
y
x
x
Compare the graph of the given quadratic function f with the graph of y = x 2 . 27) f(x) = -(x + 3)2
27)
A) a translation 3 units left and a reflection across the x-axis B) a translation 3 units right and a reflection across the x-axis C) a translation 3 units right D) a translation 3 units left
10
1 28) f(x) = (x + 5)2 - 3 3
28)
1 A) vertically stretched by a factor of and a translation 5 units left and 3 units down 3 1 B) vertically shrunken by a factor of and a translation 5 units right and 3 units down 3 1 C) vertically stretched by a factor of and a translation 5 units right and 3 units down 3 1 D) vertically shrunken by a factor of and a translation 5 units left and 3 units down 3 Solve the problem. 29)
29) Select the equation that describes the graph shown. 8
y
4
-4
8x
4
-4
B) y = (x + 2)2 - 4
A) y = (x + 4)2 + 2
C) y = x2 - 4
D) y = (x - 4)2 + 2
Graph the basic function using a solid line and the transformed function using a dotted line. 30) y = -3∣x∣
30) y 10
5
-10
-5
5
10
x
-5
-10
11
A)
B) y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
10
x
5
10
x
D) y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-10
-10
31) y
10
5
-5
-5
-5
1 31) y = - (x + 2)2 + 5 2
-10
5
5
10
x
-5
-10
12
A)
B) y
y
10
10
5
-10
-5
5
10
x
-10
10
x
10
x
-5
-10
-10
C)
D) y
y
10
10
5
-10
10
x
-10
-5
5 -5
-10
-10
Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. 32)
32) y = f(x + 5) A) (2, -1)
C) (-3, 4)
B) (7, 4)
D) (2, 9)
Determine whether the function is symmetric with respect to the y -axis, symmetric with respect to the x-axis, symmetric with respect to the origin, or none of these. 33) f(x) = -8x3 + 4x
33)
A) origin only
B) x-axis, y-axis, origin
C) x-axis only
D) y-axis only
34) f(x) = -0.05x2 + x + 8 A) y-axis only
34) B) x-axis only
C) origin only
D) none of these
Determine if the function is even, odd, or neither. 35) f(x) = -6x5 + 9x3 A) Neither
35) B) Odd
C) Even
13
Graph the point symmetric to the given point. 36) Plot (1, -4), then plot the point that is symmetric to (1, -4) with respect to the origin.
36)
y 10 8 6 4 2 -10 -8 -6 -4 -2-2 -4 -6 -8 -10
2 4 6 8 10 x
A)
B) y
y
10 8 6 4 2
10 8 6 4 2 2 4 6 8 10 x
-10 -8 -6 -4 -2-2 -4 -6 -8 -10
2 4 6 8 10 x
-10 -8 -6 -4 -2-2 -4 -6 -8 -10
C)
D) y
y
10 8 6 4 2 -10 -8 -6 -4 -2-2 -4 -6 -8 -10
10 8 6 4 2 2 4 6 8 10 x
-10 -8 -6 -4 -2-2 -4 -6 -8 -10
2 4 6 8 10 x
Determine whether the function is symmetric with respect to the y -axis, symmetric with respect to the x-axis, symmetric with respect to the origin, or none of these. 37) f(x) = 3x2 + 2
37)
A) y-axis only
B) x-axis only
C) x-axis, y-axis, origin
D) origin only
38) f(x) = (x + 5)(x + 5)
38)
A) None
B) x-axis only
C) y-axis only
D) x-axis, y-axis, origin
Graph the function. 14
1 39) f(x) = (x - 5)3 - 2 4
39)
y 10
5
-10
-5
5
10
x
-5
-10
A)
B) y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D) y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
The figure below shows the graph of a function y = f(x). Use this graph to solve the problem.
15
40) Sketch the graph of y = -f(x).
40)
y
y
(2, 4)
x
(0, -2)
x
(-4, -2)
A)
B) y
y
(-2, 4)
(2, 4)
x
x
(0, -2)
(4, -2)
C)
D) y
y
(0, 4)
(-4, 2) (0, 2) x
x (-2, -2)
(2, -4)
16
41) Sketch the graph of y = f(-x).
41)
y
(-3, 0)
y
x
(3, 0)
x
A)
B) y
y
(0, 3)
(0, 3) x
x (0, -3)
(0, -3)
C)
D) y
y
(-3, 0) (-3, 0)
(3, 0)
(3, 0)
x
x
Perform the requested operation or operations. 42) f(x) = 5x + 15, g(x) = 3x - 1 Find (f ∘ g)(x). A) 15x + 14
42) B) 15x + 10
C) 15x + 44
17
D) 15x + 20
Find the domain and range of the indicated function. 43) Find the domain and range of (fg)(x) when f(x) = 4x + 4 and g(x) = 3x - 6.
43)
A) Domain: 2, ∞ ; range: (-∞, ∞)
B) Domain: - 2, ∞ ; range: (-∞, ∞)
C) Domain: 2, ∞ ; range: (0, ∞)
D) Domain: 2, ∞ ; range: [0, ∞)
Find the requested value. 44)
44) Using the given tables find (g∘f) (3) x 3 6 4 8 f(x) 4 6 13 15
x 5 8 3 4 g(x) 9 5 8 7 A) 5
B) 13
C) 7
D) 3
Solve the problem. 45) Find (g ∘ f)(7) when f(x) = -7x - 3 and g(x) = 4x2 - 9x - 8. A) -878
B) 252
45)
C) 298
D) 11,276
Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). 1 46) h(x) = 2 x - 6 1 A) f(x) = , g(x) = x2 - 6 6
B) f(x) =
1 1 , g(x) = - 6 2 x
1 C) f(x) = , g(x) = x2 - 6 x
D) f(x) =
1 , g(x) = x - 6 x2
46)
Find the requested value. 47) The graphs of functions f and g are shown. Use these graphs to find f( 3) * g(-2). 5
y
5x
-5
A)
5
1 4
47)
y
5x
-5
-5
-5
y = f(x)
y = g(x) C) -3
B) 5
18
D) 4
Answer Key Testname: PRACT‐TEST2
1) B 2) B 3) A 4) B 5) D 6) A 7) A 8) A 9) B 10) C 11) C 12) B 13) C 14) D 15) C 16) D 17) D 18) B 19) C 20) B 21) D 22) D 23) A 24) C 25) B 26) B 27) A 28) D 29) D 30) B 31) C 32) C 33) A 34) A 35) B 36) D 37) A 38) A 39) C 40) C 41) C 42) B 43) D 44) C 45) D 46) C 47) D
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