AnswersMathematics IIIRelationships Between Quantities

Practice Test Answers

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1
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Which description could be written as a linear function?

A
ten more than the square of a number
B
eight more than twice a number
C
nine more than one divided by a number
D
three more than the product of two numbers
2
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Which equation represents a linear function?

A
y minus 5 is equal to x minus 20
B
y minus 5 is equal to x times open paren negative x plus 2 close paren
C
y times open paren y minus 1 close paren is equal to x plus 25
D
y times open paren x minus 1 close paren is equal to 9
3

Susan plans to use 120 feet of fencing to enclose a rectangular area for a garden. Which equation best models the area, y , of the rectangular garden that she creates if one side is x feet long? cap A is equal to l w

A
y is equal to open paren 60 minus x close paren times open paren 60 plus x close paren
B
y is equal to open paren 120 minus x close paren times open paren 120 plus x close paren
C
y is equal to open paren 60 minus x close paren times x
D
y is equal to open paren 120 minus x close paren times x
4

The cost of producing x soccer balls in thousands of dollars is represented by h of x is equal to 5 x plus 6 The revenue is represented by k times x is equal to 9 x minus 2 Which expression represents the profit, open paren k minus h close paren times x , of producing soccer balls?

A
4 x plus 4
B
14 x plus 4
C
4 x minus 8
D
14 x minus 8
5

Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. Which statement must be true?

A
The pool must have been the same depth at the start of the interval as it was at the end of the interval.
B
The pool must have been empty for the entire interval.
C
The pool must have been deeper at the end of the interval than it was at the start of the interval.
D
The pool must have been more shallow at the end of the interval than it was at the start of the interval.
6

If f of x is equal to x squared minus 25 and g of x is equal to x minus 5 , what is the domain of open paren f over g close paren of x ?

A
all real values of x except x is equal to 5 and x is equal to negative 5
B
all real values of x except x is equal to 5
C
all real values of x
D
all real values of x except x is equal to negative 5
7

Which function is the inverse of f of x is equal to negative 5 x minus 4 ?

A
f inverse of x is equal to negative 1 fifth x plus 4 fifths
B
f inverse of x is equal to negative 4 x plus 5
C
f inverse of x is equal to negative 1 fifth x minus 4 fifths
D
f inverse of x is equal to 4 x plus 4
8

Louis used a quadratic equation to model the height, y , of a falling object x seconds after it is dropped. Which ordered pair generated by this model should be discarded because the values are unreasonable?

A
open paren 5 comma 3 halves close paren
B
open paren 9 fourths comma 24 close paren
C
open paren 6 comma 0 close paren
D
open paren negative 4 comma 1 close paren
9

Which statement is true about f of x plus 2 is equal to 1 sixth start absolute value x minus 3 end absolute value ?

A
The graph of f of x has a vertex of open paren negative 3 comma 2 close paren .
B
The graph of f of x opens downward.
C
The graph of f of x is a horizontal compression of the graph of the parent function.
D
The graph of f of x has range of f of x is greater than or equal to negative 2 .
10

If f of x is equal to 3 x squared and g of x is equal to 4 x cubed plus 1 , what is the degree of open paren f circ g close paren times x ?

A
6
B
5
C
3
D
2
11

The cost of producing x soccer balls in thousands of dollars is represented by h of x is equal to 5 x plus 6 The revenue is represented by k times x is equal to 9 x minus 2 Which expression represents the profit, open paren k minus h close paren times x , of producing soccer balls?

A
4 x minus 8
B
14 x minus 8
C
14 x plus 4
D
4 x plus 4
12

For which pair of functions is open paren f circ g close paren times x is equal to 12 x ?

A
f of x is equal to square root of x and g of x is equal to 144 x
B
f of x is equal to 4 x and g of x is equal to 3 x
C
f of x is equal to 3 minus 4 x and g of x is equal to 16 x minus 3
D
f of x is equal to 6 x squared and g of x is equal to 2 over x
13

Which graph represents an even function?

A
Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 8 points. The points are (negative 4 comma 2), (negative 3 comma negative 1), (negative 1 comma negative 3), (0 comma 1), (1 comma 0), (2 comma negative 4), (4 comma 5), and (5 comma 4).
B
Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 7 points. The points are (negative 4 comma negative 3), (negative 3 comma negative 5), (negative 2 comma 1), (0 comma 0), (2 comma 1), (3 comma negative 5), and (4 comma negative 3).
C
Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 7 points. The points are (negative 5 comma 2), (negative 4 comma 1), (negative 3 comma 3), (negative 2 comma 5), (2 comma negative 2), (3 comma negative 5), (4 comma negative 6).
D
Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 7 points. The points are (negative 3 comma negative 6), (negative 2 comma negative 4), (negative 1 comma negative 2), (0 comma 0), (1 comma 2), (2 comma 4), and (3 comma 6).
14

Which of the following is the graph of f of x is equal to 3 start absolute value x minus 4 end absolute value plus 1 ?

A
Image with description On a coordinate plane, the scale on the x axis ranges from negative 1 to 9 in increments of 1, and the scale on the y axis ranges from negative 3 to 7 in increments of 1. The V-shaped graph opening upward has a vertex at (4 comma 1) and the graph passes through the points (3 comma 4) and (5 comma 4).
B
Image with description On a Cartesian coordinate system, the x-axis labeled from negative 8 to 2 in increments of 1 and y-axis labeled from negative 3 to 7 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (negative 4 comma negative 1). From this point, the curve opens upwards, with its left branch passing through (negative 5 comma 2) and (negative 6 comma 5), and its right branch passing through (negative 3 comma 2) and (negative 2 comma 5).
C
Image with description On a Cartesian coordinate system, the x-axis labeled from negative 9 to 1 in increments of 1 and y-axis labeled from negative 7 to 3 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (negative 4 comma 1). From this point, the curve opens downwards, with its left branch passing through (negative 5 comma negative 2) and (negative 6 comma negative 5), and its right branch passing through (negative 3 comma negative 2) and (negative 2 comma negative 5).
D
Image with description On a Cartesian coordinate system, the x-axis labeled from negative 3 to 7 in increments of 1 and y-axis labeled from negative 7 to 3 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (4 comma negative 1). From this point, the curve opens downwards, with its left branch passing through (3 comma negative 4) and (2 comma negative 7), and its right branch passing through (5 comma negative 4) and (6 comma negative 7).
15

The height in feet, h , of a model rocket t seconds after launch is given by the equation h of t is equal to 3 plus 70 t minus 16 t squared The average rate of change in h of t between t is equal to 1 second and t is equal to 3 second is 6 What does the average rate of change tell you about the rocket?

A
The rocket is traveling at a constant rate of 6 feet per second between t is equal to 1 and t is equal to 3 .
B
The rocket is traveling six times as fast when t is equal to 3 than it is when t is equal to 1 .
C
The rocket is 6 feet higher above the ground when t is equal to 3 than it is when t is equal to 1 .
D
The rocket is at a greater height when t is equal to 3 than it is when t is equal to 1 .
16

Celo used the simple interest formula cap A is equal to cap p times open paren 1 plus r t close paren to calculate the interest he earned on his savings last month. Which equation is equivalent to the simple interest formula?

A
cap p is equal to the fraction with numerator 1 plus r t and denominator cap A
B
cap p is equal to the fraction with numerator cap A and denominator 1 plus r t
C
cap p is equal to cap A plus open paren 1 plus r t close paren
D
cap p is equal to cap A minus open paren 1 plus r t close paren
17

If the function f of x is equal to m x plus b has an inverse function, which statement must be true?

A
b is not equal to 0
B
m is not equal to 0
C
m is equal to 0
D
b is equal to 0
18

The formula to determine energy is cap e is equal to 1 half m v squared What is the formula solved for v ?

A
v is equal to plus or minus square root of 2 cap e minus m end root
B
v is equal to plus or minus square root of m over 2 cap e end root
C
v is equal to plus or minus square root of 2 cap e over m end root
D
v is equal to 2 cap e minus m

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