Use the table to answer the question.

Question

l
A(l)

2 8
4 16
6 24
8 32
Kalani is trying to decide how large she wants the total area of her garden to be. The table shows some of the possibilities she is considering for the length of one side (l)
and the total area of the garden, A(l)
. Which of the following equations describes the relationship between side length and area, as outlined in this table, using function notation?

(1 point)
Responses

A(w)=l+4
upper A left parenthesis w right parenthesis equals l plus 4

A(l)=4l
upper A left parenthesis l right parenthesis equals 4 l

A(l)=2l
upper A left parenthesis l right parenthesis equals 2 l

A(w)=l+2

Answer 1

To determine the relationship between the side length (l) and the area (A(l)) based on the values in the table, we first need to analyze the provided data:

• When \( l = 2 \), \( A(2) = 8 \)
• When \( l = 4 \), \( A(4) = 16 \)
• When \( l = 6 \), \( A(6) = 24 \)
• When \( l = 8 \), \( A(8) = 32 \)

Now we can observe the area values:

• \( 8 = 4 \times 2 \)
• \( 16 = 4 \times 4 \)
• \( 24 = 4 \times 6 \)
• \( 32 = 4 \times 8 \)

This suggests that the relationship can be expressed as:

\[ A(l) = 4l \]

Thus, the correct equation that describes the relationship between side length and area in function notation is:

A(l) = 4l