AnswersMISD CR Algebraic Reasoning BCumulative Exam

Cumulative Exam — Cumulative exam Answers

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22
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The function h(x) shown is the result of adding two functions, f(x) and g(x).

Question illustration
A
Both original functions have a domain of (−∞, ∞).
B
Both original functions have a domain of [0. ∞).
C
The domain of f(x) is [0, ∞) while the domain of g(x) is (−∞, 0].
D
The domain of f(x) is (−∞, 0] while the domain of g(x) is [0, ∞).
23
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The graph of f(x) = 4x3 – 13x2 + 9x + 2 is shown below. How many roots of f(x) are rational numbers?

Question illustration
A
0
B
1
C
2
D
3
24

If m(x) = x2 + 3 and n(x) = 5x + 9, which expression is equivalent to (mn)(x)?

A
5x3 + 9x2 + 15x + 27
B
25x2 + 90x + 84
C
x2 + 5x + 12
D
5x2 + 24
25

Which equation is the inverse of y = x2 + 16?

A
y = x2 – 16
B
y = plus-or-minus StartRoot x EndRoot minus 16
Option B
C
y = plus-or-minus StartRoot x minus 16 EndRoot
Option C
D
y = x2 – 4
26

According to the Rational Root Theorem, is a potential rational root of which function?

Question illustration
A
f(x) = 4x4 – 7x2 + x + 25
B
f(x) = 9x4 – 7x2 + x + 10
C
f(x) = 10x4 – 7x2 + x + 9
D
f(x) = 25x4 – 7x2 + x + 4
27

The tables show linear functions representing the cost for purchasing different amounts of broccoli and cauliflower.

Question illustration
A
The broccoli function has the greater slope, which shows that the cost per pound of broccoli is less than the cost per pound of cauliflower.
B
The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.
C
The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is less than the cost per pound of broccoli.
D
The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is greater than the cost per pound of broccoli.
28

Consider the tables.

Question illustration
A
Table A
B
Table B
C
Table C
D
Table D
29

Which two functions are inverses of each other?

A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
30

Use the zero product property to find the solutions to the equation x2 – 15x – 100 = 0.

A
x = –20 or x = 5
B
x = –20 or x = –5
C
x = –5 or x = 20
D
x = 5 or x = 20
31

Dwight creates a table of values for a function and plots the points. He finds that one y value divided by the next y value produces the same answer each time. What kind of function did he graph?

A
linear
B
quadratic
C
square root
D
exponential
32

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.
Option D
33

The height y, in feet, of a football x seconds after it is thrown is modeled by the equation y = –16x2 + 24x + 1. What information does the zero of the equation 6 = –16x2 + 24x + 1 represent?

A
the height of the ball after 6 seconds
B
when the ball is 6 ft above the ground
C
the initial upward velocity of the ball
D
the horizontal distance traveled by the ball when it is 6 ft above the ground
34

A lake near Susan’s house is predicted to lose water every day because of a drought. The table shows the estimated water depth in feet, y, after x days of drought.

Question illustration
A
y = −0.5x + 100
B
y = −x0.5 + 100
C
y = −0.5x2 + 100
D
Option
Option D
35

The polynomial function f(x) is a fourth degree polynomial. Which of the following could be the complete list of the roots of f(x)?

A
3, 4, 5, 6
B
3, 4, 5, 6i
C
3, 4, ,
Option C
D
3, 4, 5 + i, –5 + i
36

The quadratic model f(x) = –5x2 + 200 represents the approximate height, in meters, of a ball x seconds after being dropped. The ball is 50 meters from the ground after about how many seconds?

A
2.45
B
3.16
C
5.48
D
7.07
37

Let f(x) = x + 3 and . The graph of is shown below. What is the range of ?

Question illustration
A
all real numbers except y = –3
B
all real numbers except y = 0
C
all real numbers except y = 3
D
all real numbers
38

If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?

A
On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 5) and crosses the x-axis at (1, 0).
Option A
B
On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 4), has a vertex at (0, 5), and goes through (2, negative 2)
Option B
C
On a coordinate plane, a parabola opens up. It goes through (negative 3, 7), has a vertex at (negative 1, 2), and goes through (0, 5).
Option C
D
On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)
Option D
39

The parent function f(x) = x3 is translated to form g(x), as shown on the graph. The translated function can be written in the form g(x) = (x – h)3 + k.

Question illustration
A
h = 4 k = –2
B
h = –4 k = –2
C
h = 4 k = 2
D
h = –4 k = 2
40

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?f(x) = (x3 – 3x + 1)2

A
2 roots
B
3 roots
C
6 roots
D
9 roots
41

A toy rocket is launched straight up into the air with an initial velocity of 60 ft/s from a table 3 ft above the ground. If acceleration due to gravity is –16 ft/s2, approximately how many seconds after the launch will the toy rocket reach the ground?h(t) = at2 + vt + h0

A
0.05 s
B
2.03 s
C
3.80 s
D
3.70 s

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