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

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

A(l)=4l

Answer 1

To determine the correct equation that describes the relationship between side length \( l \) and area \( A(l) \) from the given table, we can analyze the values:

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

Observing the pattern, we can see that:

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

From this, we can derive that the area \( A(l) \) is equal to \( 4 \) times the length \( l \). Therefore, the correct equation that describes the relationship is:

\[ A(l) = 4l \]

So, the answer is:

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