Question

This table shows some values of the function f(x)=
1
9
2
3
x.
x
–
2
–
1 0 1 2
f(x)
1
4
1
6
1
9
2
27
4
81
Complete the sentences.
When the x-value changes by 1 unit, the function's value changes by
. So, f(x) demonstrates that
functions change by equal
over equal intervals.

Answer 1

To fill in the sentences based on the provided function values of \( f(x) \):

1. Examine the table values you provided:

\[
\begin{align*}
x & : -2 & -1 & 0 & 1 & 2 \\
f(x) & : 1 & 4 & 1 & 6 & 1 & 9 & 2 & 27 & 4 & 81 \\
\end{align*}
\]

However, based on the appearances of \( f(x) \) values can vary widely with \( x \). If we look sequentially:

- From \( x = -2 \) to \( x = -1 \): \( f(-2) = 1 \) to \( f(-1) = 4 \) (change of 3)
- From \( x = -1 \) to \( x = 0 \): \( f(-1) = 4 \) to \( f(0) = 1 \) (change of -3)
- From \( x = 0 \) to \( x = 1\): \( f(0) =1 \) to \( f(1) = 6 \) (change of 5)
- From \( x = 1 \) to \( x = 2\): \( f(1)= 6\) to \( f(2) = 9\) (change of 3)

There is inconsistency in changes between the values you provided, indicating it wouldn't represent a function that changes at constant rates.

2. For the sentences to be filled:

"When the x-value changes by 1 unit, the function's value changes by varying amounts. So, f(x) demonstrates that non-linear functions change by unequal amounts over equal intervals."

If specific observations lead to constant changes among values indicate a linear function, they can be modified accordingly. Would you like to clarify how specifically the function data needed?