Question

The parent function y=f(x) is horizontally stretched by a factor of 3. Points on the parent function include (0,0), (1,1), (2,4), and (3,9). Complete the table for y=f(13x).(1 point)
x f(13x)
0 0
3 1
4
9

Answer 1

To determine the values of \( y = f(13x) \) for the given points after applying a horizontal stretch by a factor of 3, we first observe that stretching horizontally by a factor of 3 affects the x-coordinates inversely. Thus, for the transformation \( f(13x) \), we evaluate where \( f(x) \) would be for the given x-values.

We can rewrite the equation as \( x = \frac{t}{13} \) where \( t \) is the x-coordinate in the original function.

**Calculating the values:**

1. For \( x = 0 \):
\[
f(13 \cdot 0) = f(0) = 0
\]

2. For \( x = 3 \):
\[
13x = 13 \cdot 3 = 39 \quad \Rightarrow \quad f(39) \quad (\text{This corresponds to } t = \frac{39}{13} = 3) \quad \Rightarrow \quad f(3) = 9 \quad \Rightarrow \quad y = 1
\]

3. For \( x = 4 \):
\[
13 \cdot 4 = 52 \quad \Rightarrow \quad f(52) \quad (\text{This corresponds to } t = \frac{52}{13} = 4) \quad \Rightarrow \quad f(4) = 16 \quad \Rightarrow \quad y = 16
\]

4. For \( x = 9 \):
\[
13 \cdot 9 = 117 \quad \Rightarrow \quad f(117) \quad (\text{This corresponds to } t = \frac{117}{13} = 9) \quad \Rightarrow \quad f(9) = 81 \quad \Rightarrow \quad y = 81
\]

### Completed Table:
\[
\begin{array}{|c|c|}
\hline
x & f(13x) \\
\hline
0 & 0 \\
3 & 1 \\
4 & 16 \\
9 & 81 \\
\hline
\end{array}
\]

Therefore, the completed table for \( y = f(13x) \) is:

\[
\begin{array}{|c|c|}
\hline
x & f(13x) \\
\hline
0 & 0 \\
3 & 1 \\
4 & 16 \\
9 & 81 \\
\hline
\end{array}
\]