Question

A sandbox has a length represented by the function f(x)=x
which represents the length in yards and g(x)=x+6
represents the width in yards.

Calculate (f⋅g)(x)
showing your work.

(1 point)
f(x)=x (this represents the length in yards)
g(x)=x+6 (this represents the width in yards)

To find (f times g)(x) multiply the two functions together: (f times g)(x)=f(x) times g(x)
Substituting the definitions of f(x) and g(x) gives: (f times g)(x)=(x) times (x+6)

Now distribute x to both terms in (x+6) : (f times g)(x)= x times x + x times 6
Simplifying: (f times g)(x)=x^2 + 6x

Therefore the product is: (f times g)(x)=x^2 + 6x


The expression for (f times g)(x) is: x^2 + 6x

80 / 10000 Word Limit80 words written of 10000 allowed
Question 2
What is the situation described by (f⋅g)(x)
? (1 point)
0 / 10000 Word Limit
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Answer 1

The expression \( (f \cdot g)(x) = x^2 + 6x \) describes the area of a rectangle formed by the length and width given by the functions \( f(x) \) and \( g(x) \). Here, \( f(x) = x \) represents the length of the sandbox, while \( g(x) = x + 6 \) represents its width. The area of the sandbox, which is the product of its length and width, is given by the quadratic expression, indicating how the area changes with the varying length \( x \).