AnswersAlgebra IIModeling with Functions

Modeling with Functions — Test Answers

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What is the vertex of the absolute value function?

A
open paren negative 3 comma negative 2 close paren
B
open paren negative 3 comma 2 close paren
C
open paren 2 comma negative 3 close paren
D
open paren 2 comma 3 close paren
3

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 is a horizontal stretch of the graph of the parent function.
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 opens upward.
D
The graph of f of x has a vertex of open paren negative 4 comma 6 close paren .
5

A store uses the expression negative 2 p plus 50 to model the number of backpacks it sells per day, where the price, p , can be anywhere from 9 dollars to 15 dollars Which price gives the store the maximum amount of revenue, and what is the maximum revenue? (Revenue is equal to price times number of backpacks.)

A
12 point 0 0 dollars per backpack gives the maximum revenue; the maximum revenue is 312 point 0 0 dollars .
B
15 point 0 0 dollars per backpack gives the maximum revenue; the maximum revenue is 20 point 0 0 dollars .
C
9 point 0 0 dollars per backpack gives the maximum revenue; the maximum revenue is 32 point 0 0 .
D
12 point 5 0 dollars per backpack gives the maximum revenue; the maximum revenue is 312 point 5 0 dollars .
6

What are the domain and range of the step function with the equation? f of x is equal to negative 3 lceil x rceil

A
The domain is all integers, and the range is all integers that are multiples of 3 .
B
The domain is all integers, and the range is all real numbers.
C
The domain is all real numbers, and the range is all integers that are multiples of 3 .
D
The domain is all real numbers, and the range is all real numbers.
7

Which of the following accurately shows the range of the given function? f of x equals enlarged left-brace first row 3 comma x less than 0. Second row x squared plus 2 comma 0 less than or equal to x less than 2. Third row one half x plus 5 comma x greater than or equal to 2.

A
left bracket 2 comma infinity right parenthesis
B
left bracket 3 comma infinity right parenthesis
C
open paren negative infinity comma infinity close paren
D
left bracket 3 comma 6 right bracket
8

In the function y is equal to lfloor x rfloor minus 1 , which values of the function are equivalent?

A
f of negative 1 and f of negative 2
B
f of 2 and f of 1 point 9
C
f of negative 3 and f of negative 2 point 1
D
f of 1 and f of 0
11

Which piecewise relation defines a function?

A
y equals enlarged left-brace first row negative 3 x comma x less than negative 2. Second row 3 comma 0 less than or equal to x less than 4. Third row 2 x comma x greater than or equal to 4.
B
y equals enlarged left-brace first row negative 3 x comma x less than negative 4. Second row 3 comma negative 5 less than x less than 1. Third row 2 x comma x greater than or equal to 1.
C
y equals enlarged left-brace first row x squared comma x less than negative 2. Second row 0 comma negative 2 less than or equal to x less than or equal to 4. Third row negative x squared comma x greater than or equal to 4.
D
y equals enlarged left-brace first row x squared comma x less than or equal to negative 2. Second row 4 comma negative 2 less than x less than or equal to 2. Third row x squared plus 1 comma x greater than or equal to 2.
13

A factory produces 1 comma 250 comma 000 toys each year. The number of toys is expected to increase by about 150 percent per year. Which model can be used to find the number of toys, n (in millions), being produced in t years?

A
n is equal to the fraction with numerator 2 point 5 times 1 point 5 and denominator t , t is not equal to 0
B
n is equal to 1 point 5 t squared plus 1 point 2 5
C
n is equal to 1 point 5 t plus 1 point 2 5
D
n is equal to 1 point 2 5 times 2 point 5 to the t th power
14

The standard diameter of a golf ball is 42 point 6 7 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0 point 0 0 2 mm. Which function could represent this situation?

A
f of x is equal to 42 point 6 7 minus absolute value of x
B
f of x is equal to x minus absolute value of 42 point 6 7
C
f of x is equal to absolute value of x minus 42 point 6 7
D
f of x is equal to start absolute value 42 point 6 7 minus x end absolute value
15

What is the range of the absolute value function?

A
f of x is less than or equal to 1
B
f of x is greater than or equal to negative 4
C
f of x is less than or equal to 4
D
f of x is greater than or equal to negative 1
16

Which type of function models the data on the graph?

A
square root
B
quadratic
C
inverse variation
D
linear
18

What is the domain of the graphed function?

A
left parenthesis negative 2 comma 4 right bracket and left bracket 7 comma infinity right parenthesis
B
open paren negative 2 comma infinity close paren
C
open paren negative infinity comma 4 close paren
D
left bracket negative 2 comma 0 right bracket and open paren 7 comma infinity close paren
19

The graph represents c , the amount a phone company charges, based on m , the number of minutes the customer uses each month. If there are a maximum of 44 comma 640 minutes in a month, which equation best represents the phone company’s monthly charges?

A
c is equal to 1 fourth m plus 15 , 0 is less than or equal to m comma m is less than or equal to 44 comma 640
B
c is equal to 15 m plus 1 fourth , 0 is less than or equal to m comma m is less than or equal to 44 comma 640
C
c is equal to 15 plus 4 over m , 0 is less than m comma m is less than or equal to 44 comma 640
D
c is equal to 15 over m , 0 is less than m comma m is less than or equal to 44 comma 640
20

Which rules define the graphed function?

A
y is equal to 3 x plus 2 ; y is equal to 3 x minus 1
B
y is equal to negative 3 x plus 3 ; y is equal to x plus 3
C
y is equal to 2 x ; y is equal to negative 1 third x
D
y is equal to 2 x plus 3 ; y is equal to negative 1 third x plus 3

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