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Exam
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the slope-intercept form to write an equation of the line that passes through the given points. Use function notation where y = f(x).
1) (2, 5) and (0, 13) A) f(x) = -4x + 13 B) f(x) = 4x + 3 C) f(x) = -4x - 13 D) f(x) = -4x + 3
1)
Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x).
2) (5, -3); m = 4 A) f(x) = 4x + 5 B) f(x) = 4x - 3 C) f(x) = 4x - 15 D) f(x) = 4x - 23
2)
B-1
Use translations to graph the given function. 3) b(x) = |x - 3| + 1
A)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
B)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
C)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
D)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
3)
B-2
4) f (x) = |x + 2| A)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
B)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
C)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
D)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
4)
Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept.
5) 4x + 5y = 20
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
5)
B-3
A) y = - 4 5
x + 4
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
B) y = - 4 5
x - 4
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
C) y = - 5 4
x + 4
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
D) y = 4 5
x + 4
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
Write an equation of the line satisfying the given conditions. Write the answer in standard form.
6) The line has a slope of - 7 4
and contains the point (-7, 1).
A) 7 4
x + y = 21 4
B) y = - 7 4
x - 45 4
C) 7x + 4y = 45 D) 7x + 4y = -45
6)
Write an equation of the line satisfying the given conditions. Write the answer in standard form with no fractional coefficients.
7) Passes through (1, -3) and is parallel to the line defined by 5x - 3y = 8 A) 5x - 3y = -2 B) 5x - 3y = 1 C) 5x - 3y = -3 D) 5x - 3y = 14
7)
B-4
Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. 8) The line passes through the point (-5, -19) and has a slope of 2.
A) y = 2x - 19 B) y = -2x - 19 C) y = 2x - 9 D) y = 2x - 5 8)
Find two functions f and g such that h(x) = (f ∘ g)(x).
9) h(x) = 2
x + 1
A) f (x) = 1
x + 1 and g(x) = 2 B) f (x) = 1 and g(x) =
2 x
C) f (x) = 2 and g(x) = 1
x + 1 D) f (x) =
2 x
and g(x) = x + 1
9)
Evaluate the function for the given value of x.
10) r (x) = -5x, p (x) = x 2+ 8x, (p - r)(x)
A) (p - r)(x) = x 2 - 40x B) (p - r)(x) = x 2 + 13x
C) (p - r)(x) = x 2 - 13x D) (p - r)(x) = x 2 + 3x
10)
11) f (x) = x2 - 4x, g(x) = 3x - 2, (g ∘ f )(-3) = ? A) (g ∘ f )(-3) = -231 B) (g ∘ f )(-3) = 21 C) (g ∘ f )(-3) = 165 D) (g ∘ f )(-3) = 61
11)
12) g(x) = 6x, h(x) = x3 + 2x, (g ∘ h)(2) = ?
A) 2 3 B) 24 3 C) 8 6 D) 6 2
12)
13) f (x) = 2x, g(x) = |x - 4|, (f ∙ g)(-4) = ? A) (f ∙ g)(-4) = -64 B) (f ∙ g)(-4) = 12 C) (f ∙ g)(-4) = 64 D) (f ∙ g)(-4) = 16
13)
B-5
Find (f + g)(x) and identify the graph of f + g.
14) f (x) = x2 and g(x) = 2
A) (f + g)(x) = x2 + 2
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
B) (f + g)(x) = (x + 2)2
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
C) (f + g)(x) = x2 + 2
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
D) (f + g)(x) = (x + 2)2
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
14)
B-6
Graph the function.
15) t(x) =
x - 4, for x > 0
x2, for x ≤ 0
A)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
B)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
C)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
D)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
15)
B-7
From memory match each equation with its graph.
16) f(x) = x g(x) = 1 x
h(x) = x3
I II III
x-3 -2 -1 1 2 3
y
3
2
1
-1
-2
-3
x-3 -2 -1 1 2 3
y
3
2
1
-1
-2
-3
x-3 -2 -1 1 2 3
y
3
2
1
-1
-2
-3
x-3 -2 -1 1 2 3
y
3
2
1
-1
-2
-3
x-3 -2 -1 1 2 3
y
3
2
1
-1
-2
-3
x-3 -2 -1 1 2 3
y
3
2
1
-1
-2
-3
A) f(x), III; g(x), I; h(x), II B) f(x), I; g(x), III; h(x), II C) f(x), III; g(x), II; h(x), I D) f(x), II; g(x), III; h(x), I
16)
Find f(-x) and determine whether f is odd, even, or neither.
17) f (x) = 5x5 + 2x4
A) f (-x) = -5x5 - 2x4; f is odd.
B) f (-x) = -5x5 + 2x4; f is even.
C) f (-x) = 5x5 - 2x4; f is neither odd nor even.
D) f (-x) = -5x5 + 2x4; f is neither odd nor even.
17)
Determine if the function is linear, constant, or neither.
18) f(x) = 5 6x
A) linear B) constant C) neither
18)
The slope of a line is given. a. Determine the slope of a line parallel to the given line, if possible. b. Determine the slope of a line perpendicular to the given line, if possible.
19) m = 7 3
A) a. m = 7 3
; b. m = 3 7
B) a. m = 7 3
; b. m = - 3 7
C) a. m = 0; b. m = 3 7
D) a. m = 0; b. m = - 7 3
19)
B-8
Determine if the function is odd, even, or neither.
20) f (x) = -2x2 + 4|x5| + 3 A) even B) neither C) odd
20)
Identify the location and value of any relative maxima or minima of the function. 21)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
A) At x = -1, the function has a relative minimum of 2. At x = 1, the function has a relative maximum of 3.
B) At x = 2, the function has a relative minimum of -1. At x = 3, the function has a relative maximum of 1.
C) At x = 0, the function has a relative maximum of -2. At x = -1, the function has a relative minimum of 2. At x = 1, the function has a relative maximum of 3.
D) At x = -2, the function has a relative maximum of 0. At x = 2 the function has a relative minimum of -1. At x = 3 the function has a relative maximum of 1.
21)
B-9
Graph the equation and identify the x- and y-intercepts. 22) -2x - 3y = 6
A) x-intercept: (-2, 0); y-intercept: (0, -3)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
B) x-intercept: (-3, 0); y-intercept: (0, -2)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
C) x-intercept: (-2, 0); y-intercept: (0, 3)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
D) x-intercept: (3, 0); y-intercept: (0, -2)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
22)
Determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, origin, or none of these.
23) x = y2 + 7 A) x-axis, y-axis, and origin B) x-axis C) y-axis D) none of these
23)
B-10
Use transformations to graph the given function.
24) f(x) = -(x - 2)2 - 3 A)
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
B)
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
C)
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
D)
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
24)
B-11
25) p(x) = -4|x - 1| - 2 A)
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
B)
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
C)
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
D)
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
x-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6
y7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7
25)
B-12
26) f (x) = 1 2
x
A)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
B)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
C)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
D)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
26)
Determine the slope of the line passing through the given points. 27) (1, -4) and (-8, -8)
A) m = - 4 9
B) m = 9 4
C) m = 4 9
D) m = - 9 4
27)
B-13
Determine the slope of the line. 28)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
A) m = 3 5
B) m = - 5 3
C) m = - 3 5
D) m = 5 3
28)
Find f(x + h) - f(x)
h for the given function.
29) f (x) = x2 - 7x.
A) 1 B) 2x - 7 C) 2x + h - 7 D) 2xh + h2 - 7
29)
Evaluate the function for the given values of x. 30)
f(x) =
5x + 4, for x < -1
x2 + 2, for -1 ≤ x < 2 1, for x ≥ 2
(a) f(-1); (b) f(3) A) (a) 3; (b) 1 B) (a) 3; (b) 11 C) (a) -1; (b) 11 D) (a) -1; (b) 1
30)
Determine if the lines defined by the given equations are parallel, perpendicular, or neither. 31) -2y = 3x - 7
6x = -4y - 5 A) neither B) perpendicular C) parallel
31)
B-14
32) y = 6 5
x - 1
y = - 6 5
x + 5
A) neither B) parallel C) perpendicular
32)
Use the point-slope formula to write an equation of the line that passes through the given points. Write the answer in slope-intercept form (if possible).
33) (5, -1) and (-1, -8)
A) y = - 7 6
x - 13 2
B) y = 6 7
x - 41 6
C) y = 7 6
x - 41 6
D) y = - 6 7
x - 13 2
33)
Write the equation in slope-intercept form and determine the slope and y-intercept. 34) -5x = -2y - 10
A) y = - 5 2
x + 10; slope: - 5 2
; y-intercept: (0, 10)
B) y = - 5 2
x - 5; slope: - 5 2
; y-intercept: (0, -5)
C) y = 5 2
x + 10; slope: 5 2
; y-intercept: (0, 10)
D) y = 5 2
x - 5; slope: 5 2
; y-intercept: (0, -5)
34)
B-15
A function g is given. Identify the parent function. Then use the steps for graphing multiple transformations of functions to list, in order, the transformations applied to the parent function to obtain the graph of g.
35) g(x) = 3
x + 4 + 2
A) Parent function: f (x) = 1 x
; Shift the graph of f to the left 4 units, stretch the graph
vertically by a factor of 3, and shift the graph upward by 2 units.
B) Parent function: f (x) = 1 x
; Shift the graph of f to the right 4 units, stretch the graph
vertically by a factor of 3, and shift the graph downward by 2 units.
C) Parent function: f (x) = 1 x
; Shift the graph of f to the left 4 units, shrink the graph
vertically by a factor of 1 3
, and shift the graph upward by 2 units.
D) Parent function: f (x) = 1 x
; Shift the graph of f to the right 4 units, shrink the graph
vertically by a factor of 1 3
, and shift the graph downward by 2 units.
35)
B-16
Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. 36)
x-5 -4 -3 -2 -1 1 2 3 4 5
y 5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y 5
4
3
2
1
-1
-2
-3
-4
-5
A) a. (-∞, 3) ∪ (3, ∞) b. never decreasing c. (-2, 2)
B) a. (-∞, -2) ∪ (2, ∞) b. never decreasing c. (-2, 2)
C) a. never increasing b. (-∞, -2) ∪ (2, ∞) c. (-2, 2)
D) a. (-5, ∞) b. (-∞, -5) c. never constant
36)
Match the function with the graph. 37)
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
x-5 -4 -3 -2 -1 1 2 3 4 5
y5
4
3
2
1
-1
-2
-3
-4
-5
A) f(x) = -x - 1 for x ≤ 1 B) f(x) = -x - 1 for x ≥ -2 C) f(x) = -x - 1 for x ≥ 1 D) f(x) = -x - 1 for x ≤ -2
37)
B-17
Answer Key Testname: MATH 1314 TEST 2 FALL 2022
1) A 2) D 3) A 4) B 5) A 6) D 7) D 8) C 9) D
10) B 11) D 12) D 13) A 14) C 15) B 16) B 17) D 18) C 19) B 20) A 21) D 22) B 23) B 24) B 25) A 26) C 27) C 28) B 29) C 30) A 31) C 32) A 33) C 34) D 35) A 36) B 37) D
B-18
