AnswersAlgebra IIMathematical Modeling

Mathematical Modeling — Test Answers

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1
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Which rules define the graphed function?

A
y is equal to 2 x plus 3 ; y is equal to negative 1 third x plus 3
B
y is equal to 2 x ; y is equal to negative 1 third x
C
y is equal to negative 3 x plus 3 ; y is equal to x plus 3
D
y is equal to 3 x plus 2 ; y is equal to 3 x minus 1
2
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Which characteristics do the functions have in common? Choose two correct answers.

A
domain
B
y -intercept
C
range
D
x -intercept
E
minimum
3

What is the domain of the absolute value function?

A
x is less than or equal to negative 4
B
open paren negative infinity comma negative 4 close paren
C
open paren negative infinity comma plus infinity close paren
D
x is greater than or equal to 2
4

Which rules define the graphed function?

A
y is equal to x ; x is equal to 5
B
y is equal to x plus 2 ; y is equal to 5
C
y is equal to x plus 2 ; x is equal to 5
D
y is equal to x ; y is equal to 5
5

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 vertex of open paren negative 4 comma 6 close paren .
C
The graph of f of x has a domain of x is less than or equal to negative 6 .
D
The graph of f of x opens upward.
6

In a certain country, a letter up to 1 ounce requires postage in the amount of 0 point 4 2 dollars , and each additional ounce (or fraction of an ounce) has an additional cost. The function represents the cost of mailing one letter with a weight of x ounces in this country. f of x is equal to 0 point 4 2 plus 0 point 2 0 lceil x minus 1 rceil Josiah has two letters. The first weighs 2 point 9 ounces, and the second weighs 4 point 1 ounces. What is the total amount Josiah can expect to pay for postage?

A
1 point 6 4 dollars
B
1 point 6 2 dollars
C
1 point 8 4 dollars
D
2 point 0 4 dollars
7

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 start absolute value 42 point 6 7 minus x end absolute value
C
f of x is equal to x minus absolute value of 42 point 6 7
D
f of x is equal to absolute value of x minus 42 point 6 7
8

Consider the functions f of x is equal to 3 x squared , g of x is equal to 1 over 3 x , and h of x is equal to 3 x Which statements accurately compare the domain and range of the functions? Choose two correct answers.

A
The range of all three functions is all real numbers.
B
The domain of all three functions is all real numbers.
C
The range of f of x and h of x is all real numbers, but the range of g of x is all real numbers except 0 .
D
All of the functions have a unique range.
E
The domain of f of x and h of x is all real numbers, but the domain of g of x is all real numbers except 0 .
9

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
open paren negative infinity comma infinity close paren
C
left bracket 3 comma infinity right parenthesis
D
left bracket 3 comma 6 right bracket
10

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 real numbers, and the range is all integers that are multiples of 3 .
B
The domain is all integers, and the range is all integers that are multiples of 3 .
C
The domain is all integers, and the range is all real numbers.
D
The domain is all real numbers, and the range is all real numbers.
11

If f of x is equal to 3 lfloor x minus 2 rfloor , what is f of 5 point 9 ?

A
11
B
9
C
10
D
12
12

The equation of the piecewise defined function f of x is shown. What is the value of f of 1 ? f of x equals enlarged left-brace first row x squared plus 1 comma negative 4 less than or equal to x less than 1. Second row negative x squared comma 1 less than or equal to x less than 2. Third row 3 x comma x greater than or equal to 2.

A
f of 1 is equal to negative 2
B
f of 1 is equal to 3
C
f of 1 is equal to 2
D
f of 1 is equal to negative 1
13

A company manufactures 16 -oz boxes of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0 point 1 5 oz, the production is stopped. What is the range of acceptable values for production to continue?

A
15 point 1 5 oz to 16 point 0 0 oz
B
15 point 8 5 oz to 16 point 0 0 oz
C
16 point 1 5 oz to 16 point 4 5 oz
D
15 point 8 5 oz to 16 point 1 5 oz
14

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.
15

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 1 and f of 0
D
f of negative 3 and f of negative 2 point 1
16

What is the vertex of the absolute value function?

A
open paren 2 comma 3 close paren
B
open paren 2 comma negative 3 close paren
C
open paren negative 3 comma 2 close paren
D
open paren negative 3 comma negative 2 close paren
17

For which x -values is the graph discontinuous?

A
start set dot dot dot minus 3 comma negative 2 comma negative 1 comma 0 comma 1 comma 2 comma 3 comma dot dot dot end set
B
start set dot dot dot minus 4 comma negative 2 comma 0 comma 2 comma 4 comma dot dot dot end set
C
start set dot dot dot minus 3 comma negative 1 comma 1 comma 3 comma dot dot dot end set
D
start set dot dot dot minus 3 comma negative 1 comma 0 comma 1 comma 3 comma dot dot dot end set
18

If all city buses carry the same number of passengers, what is the least number of buses needed to carry 710 passengers?

A
12
B
10
C
11
D
5
19

Which statements can be used to compare the characteristics of the functions? Choose three correct answers.

A
f of x has the greatest maximum.
B
g of x has the smallest minimum value.
C
h of x has the greatest x - intercept.
D
All three functions share the same y -intercept.
E
All three functions share the same domain.
20

What is the domain of the graphed function?

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

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