Functions and Their Inverses — Test Answers

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If A times x is equal to 2 x minus 4 and b times x is equal to x plus 2 , which of the following expressions produces a quadratic function?

A
open paren A minus b close paren times x
B
open paren A over b close paren times x
C
A b times x
D
open paren A plus b close paren times x
3

If f of x is equal to absolute value of x plus 9 and g of x is equal to negative 6 , which describes the range of open paren f plus g close paren of x ?

A
open paren f plus g close paren of x is less than or equal to 3 for all values of x
B
open paren f plus g close paren of x is greater than or equal to 6 for all values of x
C
open paren f plus g close paren of x is less than or equal to 6 for all values of x
D
open paren f plus g close paren of x is greater than or equal to 3 for all values of x
4

The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation start absolute value x minus 72 point 5 end absolute value is equal to 4 What are the minimum and maximum temperatures in the house?

A
72 point 5 degrees Fahrenheit F and 74 point 5 degrees Fahrenheit F
B
70 point 5 degrees Fahrenheit F and 74 point 5 degrees Fahrenheit F
C
72 point 5 degrees Fahrenheit F and 76 point 5 degrees Fahrenheit F
D
68 point 5 degrees Fahrenheit F and 76 point 5 degrees Fahrenheit F
5

Which expression is equivalent to open paren f plus g close paren of 4 ?

A
f of 4 plus g of 4
B
f of open paren 4 plus g of 4 close paren
C
4 times open paren f of x plus g of x close paren
D
f of x plus g of 4
6

Which statement is true about f of x is equal to negative 2 thirds start absolute value x plus 4 end absolute value minus 6 ?

A
The graph of f of x has a vertex of open paren negative 4 comma 6 close paren .
B
The graph of f of x has a domain of x is less than or equal to negative 6 .
C
The graph of f of x is a horizontal stretch of the graph of the parent function.
D
The graph of f of x opens upward.
9

Which function has an inverse that is also a function?

A
f of x is equal to start absolute value x plus 2 end absolute value
B
k times x is equal to negative 9 x squared
C
g of x is equal to 2 x minus 3
D
w times x is equal to negative 20
10

The function h of x is given. h of x is equal to open paren 3 comma negative 5 close paren comma open paren 5 comma negative 7 close paren comma open paren 6 comma negative 9 close paren comma open paren 10 comma negative 12 close paren comma open paren 12 comma negative 16 close paren Which of the following gives h inverse of x ?

A
start set open paren 3 comma negative 5 close paren comma open paren 5 comma negative 7 close paren comma open paren 6 comma negative 9 close paren comma open paren 10 comma negative 12 close paren comma open paren 12 comma negative 16 close paren end set
B
start set open paren 3 comma 5 close paren comma open paren 5 comma 7 close paren comma open paren 6 comma 9 close paren comma open paren 10 comma 12 close paren comma open paren 12 comma 16 close paren end set
C
start set open paren 5 comma 3 close paren comma open paren 7 comma 5 close paren comma open paren 9 comma 6 close paren comma open paren 12 comma 10 close paren comma open paren 16 comma 12 close paren end set
D
start set open paren negative 5 comma 3 close paren comma open paren negative 7 comma 5 close paren comma open paren negative 9 comma 6 close paren comma open paren negative 12 comma 10 close paren comma open paren negative 16 comma 12 close paren end set
12

Kari and Samantha have determined that their water-balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. Which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal?

A
start absolute value x minus 45 end absolute value is equal to 3 ; minimum angle: 42 degrees
B
start absolute value x minus 3 end absolute value is equal to 45 ; minimum angle: 42 degrees
C
start absolute value x minus 45 end absolute value is equal to 3 ; minimum angle: 45 degrees
D
start absolute value x minus 3 end absolute value is equal to 45 ; minimum angle: 45 degrees
13

How is the graph of y is equal to open paren x minus 1 close paren squared minus 3 transformed to produce the graph of y is equal to 1 half times open paren x plus 4 close paren squared ?

A
The graph is stretched horizontally by a factor of 1 half , translated left 5 units, and translated down 3 units.
B
The graph is translated left 5 units, compressed vertically by a factor of 1 half , and translated up 3 units.
C
The graph is stretched vertically by a factor of 1 half , translated left 5 units, and translated up 3 units.
D
The graph is translated left 5 units, compressed horizontally by a factor of 1 half , and translated down 3 units.
14

Which number line represents the solutions to negative 2 absolute value of x is equal to negative 6 ?

A
Image with description A number line labeled from negative 8 to positive 8 in increments of 1. Two points, one at negative 8 and one at negative 4.
B
Image with description A number line labeled from negative 8 to positive 8 in increments of 1. Two points, one at negative 6 and one at negative 2.
C
Image with description A number line labeled from negative 8 to positive 8 in increments of 1. Two points, one at negative 4 and one at positive 4.
D
Image with description A number line labeled from negative 8 to positive 8 in increments of 1. Two points, one at negative 3 and one at positive 3.
16

Johan found that the equation negative 2 start absolute value 8 minus x end absolute value minus 6 is equal to negative 12 had two possible solutions: x is equal to 5 and x is equal to negative 11 Which explains whether his solutions are correct?

A
He is not correct because there is only one solution: x is equal to 5 .
B
He is not correct because he made a sign error.
C
He is correct because both solutions satisfy the equation.
D
He is not correct because there are no solutions.
18

If f of x is equal to 1 ninth x minus 2 , what is f inverse of x ?

A
f inverse of x is equal to negative 2 x plus 1 ninth
B
f inverse of x is equal to 1 ninth x plus 2
C
f inverse of x is equal to 9 x plus 2
D
f inverse of x is equal to 9 x plus 18
19

Based on the family the graph belongs to, which equation could represent the graph?

A
y is equal to the fraction with numerator 1 and denominator x plus 2 plus 3
B
y is equal to x cubed plus 3
C
y is equal to 0 point 2 to the x th power plus 3
D
y is equal to log x plus 3
20

The graph of y is equal to x cubed is transformed as shown in the graph. Which equation represents the transformed function?

A
y is equal to negative x cubed minus 4
B
y is equal to open paren negative x minus 4 close paren cubed
C
y is equal to x cubed minus 4
D
y is equal to open paren x minus 4 close paren cubed
21

What is the vertex of the absolute value function?

A
open paren 1 comma 4 close paren
B
open paren 4 comma negative 1 close paren
C
open paren 4 comma 1 close paren
D
open paren 1 comma negative 4 close paren

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