AnswersAlgebraic ReasoningSolving Quadratic Equations — TestQuestion 9
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Solving Quadratic Equations — Test

Question 9 • Algebraic Reasoning

A shipping company charges based on calculations of the volume of a rectangular box and the sum of the dimensions of the box. A square rectangular prism has a side length represented by the linear function f of x , and a height represented by the linear function g of x x cap v times x is equal to open paren f times f times g close paren times x cap s times x is equal to open paren f plus f plus g close paren times x 3 15 8 4 24 10 5 35 12 6 48 14 Which statement describes the combined functions cap v times x and cap s times x ?

Answer
A
The sum function is linear but the volume function is not.
B
The volume function is linear but the sum function is not.
C
Both the volume function and the sum function are linear.
D
Neither the volume function nor the sum function is linear.

Explanation

As x increases by 1, the sum function’s values go from 8 to 10 to 12 to 14, increasing by 2 each time. That constant rate of change means the sum function is linear. The volume values are 15, 24, 35, and 48, whose increases are 9, 11, and 13, so the volume function is not linear. Therefore, the statement that the sum function is linear but the volume function is not is correct.

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