Mathematical Modeling — Test Answers

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

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How do the functions in the tables compare?

The rockets traveled the same height in the air, but the rocket for group B was in the air for a longer time.

Since the maximums occurred at the same x -value, the rockets followed the same path.

The rockets were in the air for the same amount of time, but the rocket for group B went higher in the air.

Since the x -intercepts are the same for both functions, the rockets followed the same path.

Which characteristics do the functions have in common? Choose two correct answers.

minimum

range

x -intercept

y -intercept

domain

Which function has the greater slope and what does it indicate?

The math function has the greater slope, which shows that the estimated time per question for math is greater than the estimated time per question for language arts.

The language arts function has the greater slope, which shows that the estimated time per question for language arts is less than the estimated time per question for math.

The math function has the greater slope, which shows that the estimated time per question for math is less than the estimated time per question for language arts.

The language arts function has the greater slope, which shows that the estimated time per question for language arts is greater than the estimated time per question for math.

How do the functions in the table compare?

Since x -intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.

Since y -intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.

Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.

Which statements can be used to compare the functions? Choose two correct answers.

Only f of x has an x -intercept.

g of x has the greatest maximum.

All three functions have a y -intercept.

All three functions have the same domain values.

All three functions have the same range values.

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

All three functions share the same domain.

f of x has an all negative domain.

All three functions share the same range.

g of x has the greatest maximum value.

h of x has a range of all negative numbers.

What are the domain and range of the step function?

domain = {all real numbers}, range = {all real numbers}

domain is equal to dot dot dot minus 5 comma negative 2 comma 1 comma 4 comma dot dot dot , range is equal to dot dot dot minus 4 comma negative 1 comma 2 comma 5 comma dot dot dot

domain = {all real numbers}, range is equal to dot dot dot minus 4 comma negative 1 comma 2 comma 5 comma dot dot dot

domain = {all integers}, range = {all real numbers}

What is the vertex of the absolute value function?

open paren 2 comma 3 close paren

open paren negative 3 comma negative 2 close paren

open paren negative 3 comma 2 close paren

open paren 2 comma negative 3 close paren

What is the vertex of the absolute value function?

open paren 1 comma 4 close paren

open paren 4 comma 1 close paren

open paren 1 comma negative 4 close paren

open paren 4 comma negative 1 close paren

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?

f of x is equal to 42 point 6 7 minus absolute value of x

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

f of x is equal to x minus absolute value of 42 point 6 7

f of x is equal to absolute value of x minus 42 point 6 7

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?

1 point 8 4 dollars

2 point 0 4 dollars

1 point 6 4 dollars

1 point 6 2 dollars

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.

The range of all three functions is all real numbers.

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 .

All of the functions have a unique range.

The domain of all three functions is all real numbers.

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 .

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

f of negative 3 and f of negative 2 point 1

f of 2 and f of 1 point 9

f of negative 1 and f of negative 2

f of 1 and f of 0

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

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 ?

The graph of f of x has a vertex of open paren negative 4 comma 6 close paren .

The graph of f of x opens upward.

The graph of f of x has a domain of x is less than or equal to negative 6 .

The graph of f of x is a horizontal stretch of the graph of the parent function.

A shipping company charges 6 dollars to ship a package that weighs up to 1 pound and 2 dollars for each additional pound or portion of a pound. Which equation represents the cost, in dollars, of shipping a package that weighs x pounds?

f of x is equal to 6 plus 2 lceil x minus 1 rceil , where x is greater than 0

f of x is equal to 6 plus 2 lfloor x minus 1 rfloor , where x is greater than 0

f of x is equal to 6 plus 2 lceil x plus 1 rceil , where x is greater than 0

f of x is equal to 6 plus 2 lfloor x plus 1 rfloor , where x is greater than 0

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

The domain is all real numbers, and the range is all real numbers.

The domain is all integers, and the range is all real numbers.

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

The domain is all integers, and the range is all integers that are multiples of 3 .

Given the function f of x is equal to 0 point 5 start absolute value x minus 4 end absolute value minus 3 , for what values of x is f of x is equal to 7 ?

x is equal to negative 24 , x is equal to 16

x is equal to negative 1 , x is equal to 9

x is equal to negative 16 , x is equal to 24

x is equal to 1 , x is equal to negative 9

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?

15 point 8 5 oz to 16 point 0 0 oz

15 point 1 5 oz to 16 point 0 0 oz

15 point 8 5 oz to 16 point 1 5 oz

16 point 1 5 oz to 16 point 4 5 oz

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Mathematical Modeling — Test Answers

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