Write a rule for the linear function in the table.

x

f(x)
–4

16
0

0
4

–16
8

–32
A. f(x) = –4x
B. f(x) = x + 16
C. f(x) = 4x
D. f(x) = -1/4x

Looks like -4x

To determine the rule for the linear function in the table, we need to find the relationship between the inputs (x) and the outputs (f(x)).

Looking at the table, we can notice that for each value of x, the corresponding value of f(x) is obtained by multiplying x by a constant value.

Let's take the first row of the table:

x = -4, f(x) = 16

From -4 to 16, it looks like we multiplied x by -4 to get f(x).

Now let's try with the second row:

x = 0, f(x) = 0

We can see that multiplying 0 by any number will always give us 0. Therefore, we don't need to consider the constant value.

Next row:

x = 4, f(x) = -16

Now it seems that we multiplied x by -4 to get f(x), just like in the first row.

Finally, the last row:

x = 8, f(x) = -32

Again, multiplying x by -4 gives us f(x).

Based on all the rows, it is clear that the constant value we need to multiply x by to get f(x) is -4.

Therefore, the rule for the linear function in the table is:

f(x) = -4x

The correct answer is A. f(x) = -4x.