MATH 0350
TEST 1 REVIEW
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Decide whether the relation is a function.
1) {(-6, -4), (-3, -9), (-1, -1), (-1, 7)}
A) Function
1)
B) Not a function
Solve the problem.
2) Find g(a + 1) when g(x) = 2x + 2.
A) 2a + 4
2)
1
C) a + 2
2
B) 2a + 2
D) 2a - 1
Provide an appropriate response.
3) Complete the following statement: The notation f(8) means
A) the value of the dependent variable when the independent variable is 8.
B) f equals 8.
C) the variable f times 8 or 8f.
D) the value of the independent variable when the dependent variable is 8.
Decide whether the relation is a function.
4) x -2 2 5 9 10
y -2 2 -9 -2 3
A) Function
3)
4)
B) Not a function
5)
5)
A) Function
B) Not a function
6)
6)
-3
-2
-17
A) Function
-16
11
-6
B) Not a function
Give the domain and range of the relation.
7)
7)
A) Domain: {4, 5, 7}; Range: {8, 12, 13}
C) Domain: {5, 8, 13}; Range: {4, 7, 12}
B) Domain: {4, 7, 12}; Range: {5, 8, 13}
D) None of the above
1
8)
8)
A) Domain: {5, 13}; Range: {4, 7, 12}
C) Domain: {4, 5, 7}; Range: {12, 13}
B) Domain: {4, 7, 12}; Range: {5, 13}
D) None of the above
Determine whether the relation defines y as a function of x. Give the domain.
9) y2 = 3x
A) Function; domain: (-∞, 0]
C) Function; domain: (-∞, ∞)
10) y =
9)
B) Not a function; domain: [0, ∞)
D) Not a function; domain: (-∞, 0]
-6
x + 13
10)
A) Function; domain: (-13, 13)
B) Function; domain: (-∞, -13) ∪ (-13, ∞)
C) Not a function; domain: (-∞, ∞)
D) Not a function; domain: (-∞, -13) ∪ (-13, 0)
Solve the problem.
11) The mathematical model C(x) = 200x + 100,000 represents the cost in dollars a company has in
manufacturing x items during a month. Based on this, how much does it cost to produce 300 items?
A) $160,000
B) $500.00
C) $60,000
D) $1.67
Give the domain and range of the relation.
12) {(3, 7), (-3, -8), (-7, -5), (6, 0)}
A) Domain: {-8, -7, -5, -3}; Range: {3, 6, 7}
C) Domain: {-8, -5, 0, 7}; Range: {-7, -3, 3, 6}
12)
B) Domain: {-7, -3, 3, 6}; Range: {-8, -5, 0, 7}
D) Domain: {3, 6, 7}; Range: {-8, -7, -5, -3}
Graph the linear or constant function. Give the domain and range.
13) h(x) = -6
6
y
4
2
-6
-4
-2
2
4
11)
6 x
-2
-4
-6
2
13)
A) domain: {-6}; range: (-∞, ∞)
B) domain: {-6}; range: (-∞, ∞)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6
x
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
C) domain: (-∞, ∞); range: {-6}
-4
x
6
x
y
6
6
4
4
2
2
-2
6
D) domain: (-∞, ∞); range: {-6}
y
-6
4
2
4
6
x
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
Decide whether the relation is a function.
14) {(-1, -9), (1, -4), (6, 1), (9, 6), (12, -2)}
A) Function
B) Not a function
Evaluate the composition of functions.
15) Let f(x) = 5x + 3 and g(x) = x + 7. Find (g ∘ f)(4).
A) 58
B) 30
C) 253
4
14)
15)
Provide the appropriate response.
16) What is the domain of the square root function, f(x) = x?
A) (-∞, 0]
B) (-∞, ∞)
C) [0, ∞)
D) 34
16)
D) [0,
∞)
For the given pair of functions, find the indicated value or expression.
17) Given f(x) = 3x - 4 and g(x) = -7x2 - 16x + 8, find (f - g)(x).
A) -7x2 + 19x + 12
B) 7x2 + 19x - 12
17)
C) -7x2 - 13x + 4
D) 7x2 - 13x - 12
18) Given f(x) = 3x - 4 and g(x) = -8x2 - 16x + 10, find (f + g)(x).
A) 8x2 - 5x - 14
B) -9x2 - 13x - 6
C) -8x2 + 13x + 6
D) -8x2 - 13x + 6
19) Given f(x) = x2 - 5 and g(x) = 2x + 3, find (f + g)(-5).
A) 13
B) x2 + 2x - 2
3
18)
19)
C) -5x2 - 10x + 10
D) 23
20) Given f(x) = 6x + 8 and g(x) = x - 2, find (f - g)(-1).
A) 5x + 10
B) 1
21) Let f(x) = x2 - 1x - 56 and g(x) = x - 8, find
A) x + 7, x ≠ -8
20)
C) -5x - 10
D) 5
f
(x).
g
21)
B) x + 8, x ≠ 7
C) x + 7, x ≠ 8
D) x + 1, x ≠ 0
Provide the appropriate response.
22) The lowest point on the graph of f(x) = |x| + 1 has what coordinates?
A) (0, 1)
B) (0, - 1)
C) (1, 0)
22)
D) (- 1, 0)
Without plotting points, match the function defined by the absolute value expression with its graph.
23) f(x) = x + 3 + 3
A)
B)
y
y
5
5
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1
-1
23)
1
2
3
4
5
x
-5 -4 -3 -2 -1
-1
-2
-2
-3
-3
-4
-4
-5
-5
C)
1
2
3
4
5
x
1
2
3
4
5
x
D)
y
y
5
5
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1
-1
1
2
3
4
5
x
-5 -4 -3 -2 -1
-1
-2
-2
-3
-3
-4
-4
-5
-5
Find (f ∘g)(x) for the given functions f(x) and g(x).
24) f(x) = 3x - 2 and g(x) = 2x - 7
A) 12x - 9
B) 6x - 23
24)
C) 3x + 2
D) 6x - 11
Find all numbers not in the domain of the function.
x-1
25) f(x) =
2x + 4
A) - 2, 1
25)
B) None
C) 2
4
D) - 2
26) f(x) =
x-5
3-x
A) -3
27) f(x) =
B) 3, 5
C) 3
D) None
5
x+2
A) None
28) f(x) =
26)
27)
B) -2
C) 2
D) 0
x-7
8
A) -7
28)
B) 0
C) 7
D) None
Find all numbers that are not in the domain of the function. Then give the domain using set notation.
x-2
29) f(x) =
6
A) 6; {x x ≠ 6}
30) f(x) =
B) none; (-∞, ∞)
C) 2; {x x ≠ 2}
D) 0; {x x ≠ 0}
1
x-4
30)
A) -1; {x|x ≠ -1}
C) -4, 4; {x|x ≠ -4, 4}
B) 4; {x|x ≠ 4}
D) none; (-∞, ∞)
For the given pair of functions, find the indicated value or expression.
f
31) Let f(x) = x2 - 5x - 24 and g(x) = x - 8, find
(x).
g
A) x + 3, x ≠ 8
B) x + 5, x ≠ 0
C) x + 8, x ≠ 3
31)
D) x + 3, x ≠ -8
Evaluate the composition of functions.
32) Let f(x) = x2 + 3 and g(x) = 4x + 6. Find (g ∘ f)(5).
A) 106
29)
32)
B) 679
C) 34
33) Let f(x) = x2 + 2 and g(x) = 3x + 6. Find (f ∘ g)(7).
A) 731
B) 57
D) 118
33)
C) 159
5
D) 147
Graph the linear or constant function. Give the domain and range.
34) f(x) = 4x - 6
6
34)
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
A) domain: (-∞, ∞); range: (-∞, ∞)
B) domain: (-∞, ∞); range: (-∞, ∞)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6
x
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
C) domain: (-∞, ∞); range: (-∞, ∞)
-4
x
y
6
6
4
4
2
2
-2
6
D) domain: (-∞, ∞); range: (-∞, ∞)
y
-6
4
2
4
6
x
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
6
4
6
x
35) g(x) = x + 6
35)
6
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
A) domain: (-∞, ∞); range: (-∞, ∞)
B) domain: (-∞, ∞); range: (-∞, ∞)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6
x
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
C) domain: (-∞, ∞); range: (-∞, ∞)
-4
6
4
4
2
2
2
4
6
x
-6
-2
2
-2
-4
-4
-6
-6
4
6
x
36)
6
y
4
2
-4
-4
-2
36) h(x) = -4
-6
x
y
6
-2
6
D) domain: (-∞, ∞); range: (-∞, ∞)
y
-6
4
-2
2
4
6 x
-2
-4
-6
7
A) domain: (-∞, ∞); range: {-4}
B) domain: (-∞, ∞); range: {-4}
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6
x
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
C) domain: {-4}; range: (-∞, ∞)
-4
x
6
x
y
6
6
4
4
2
2
-2
6
D) domain: {-4}; range: (-∞, ∞)
y
-6
4
2
4
6
x
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
4
Solve the problem.
37) If the height of a rectangular solid is held constant, the volume varies jointly with the length and
the width. If the volume is 144 cubic inches when the length is 9 inches and the width is 4 inches,
find the volume when the length is 8 inches and the width is 5 inches.
A) 120 in.3
B) 160 in. 3
C) 180 in. 3
D) 128 in. 3
37)
Determine whether the variation between the indicated quantities is direct or inverse.
38) The time it takes to drive 100 miles and the speed at which you drive
A) Inverse
B) Direct
38)
Solve the problem.
39) If m varies directly as p, and m = 63 when p = 9, find m when p is 5.
A) 25
B) 35
C) 81
39)
D) 49
Determine whether the equation represents direct, inverse, joint, or combined variation.
4
40) y =
x
A) Joint
B) Inverse
C) Direct
8
40)
D) Combined
Solve the problem.
41) The current I in an electrical conductor varies inversely as the resistance R of the conductor. The
current is 8 amperes when the resistance is 895 ohms. What is the current when the resistance is 848
ohms?
A) 7.6 amps
B) 0.13 amps
C) 0.12 amps
D) 8.4 amps
42) If x varies inversely as v, and x = 35 when v = 3, find x when v = 21.
A) 15
B) 7
C) 5
42)
D) 9
43) The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical
container 4 cm on a side is 192 g, find the weight of the liquid in a cubical container 3 cm on a side.
A) 9 g
B) 27 g
C) 15 g
D) 81 g
Determine whether the variation between the indicated quantities is direct or inverse.
44) The number of hours worked by an hourly worker and the amount of her paycheck
A) Inverse
B) Direct
9
41)
43)
44)
Answer Key
Testname: MATH 0107 TEST 1 REVIEW
1) B
2) A
3) A
4) A
5) B
6) B
7) B
8) B
9) B
10) B
11) A
12) B
13) D
14) A
15) B
16) C
17) B
18) D
19) A
20) D
21) C
22) A
23) C
24) B
25) D
26) C
27) B
28) D
29) B
30) B
31) A
32) D
33) A
34) D
35) A
36) A
37) B
38) A
39) B
40) B
41) D
42) C
43) D
44) B
10