AnswersAlgebraic ReasoningOperations with Multiple Functions — QuizQuestion 7
7
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Operations with Multiple Functions — Quiz

Question 7 • Algebraic Reasoning

The table shows the functions representing the length and width of a rectangle. x Length f of x is equal to x plus 3 Width g of x is equal to x plus 2 1 4 3 2 5 4 3 6 5 4 7 6 The perimeter of the rectangle when x is equal to 3 is 22 Which equation can be used to represent the perimeter of the rectangle, cap p times x ?

Answer
A
cap p times x is equal to 2 open paren f times g close paren x
B
cap p times x is equal to open paren f times g close paren of x
C
cap p times x is equal to 2 open paren f plus g close paren x
D
cap p times x is equal to open paren f plus g close paren of x

Explanation

A rectangle’s perimeter is twice the sum of its length and width, so the function is p(x) = 2(f(x) + g(x)). When x = 3, f(3) = 6 and g(3) = 5, giving a perimeter of 2(6 + 5) = 22, as stated. Therefore, the equation is 2(f + g)(x), choice C.

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