Question

Use the table to answer the 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)=4l
upper A left parenthesis l right parenthesis equals 4 l

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

Answer 1

Given f(x)=4(x−3)2
, what is f(2)
?(1 point)
Responses

4
4

16
16

−4
negative 4

−16

Answer 2

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.

From the table:
- For \( l = 2 \), \( A(2) = 8 \)
- For \( l = 4 \), \( A(4) = 16 \)
- For \( l = 6 \), \( A(6) = 24 \)
- For \( l = 8 \), \( A(8) = 32 \)

We can observe that as \( l \) increases, the total area \( A(l) \) appears to increase in a linear fashion.

To identify the relationship, let's look at the changes in \( A(l) \):

1. When \( l = 2 \), \( A(2) = 4 \times 2 = 8 \)
2. When \( l = 4 \), \( A(4) = 4 \times 4 = 16 \)
3. When \( l = 6 \), \( A(6) = 4 \times 6 = 24 \)
4. When \( l = 8 \), \( A(8) = 4 \times 8 = 32 \)

From this, we can see that the area is four times the side length (which can be interpreted as a scaling factor).

Thus, the equation that describes this relationship is:

\[
A(l) = 4l
\]

Therefore, the correct response is:

**A(l) = 4l**