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

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

A(w)=l+2
upper A left parenthesis w right parenthesis equals l plus 2

A(w)=l+4

Answer 1

To determine the correct equation that describes the relationship between the side length \( l \) and the total area \( A(l) \), we can analyze the values provided in the table.

The table shows the following pairs:

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

Now, let's look for a pattern.

1. Calculate \( A(l) \) as a function of \( l \):
   • For \( l = 2 \): \( 2 \times 4 = 8 \)
   • For \( l = 4 \): \( 4 \times 4 = 16 \)
   • For \( l = 6 \): \( 6 \times 4 = 24 \)
   • For \( l = 8 \): \( 8 \times 4 = 32 \)

From the analysis above, we see that the total area \( A(l) \) can be described by the equation:

\[ A(l) = 4l \]

Thus, the correct response is:

A(l) = 4l