Question

The patent 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(1/3x)
x f(1/3x)
0 0
3 1
__ 4
___ 9

Answers

Answered by GPT-4o mini
To find the values of \( f(1/3x) \) for the specified parent function \( y = f(x) \), we will use the information given about the parent function and the horizontal stretch.

The original points on the parent function \( f(x) \) are:
- \( (0, 0) \)
- \( (1, 1) \)
- \( (2, 4) \)
- \( (3, 9) \)

When we horizontally stretch the function by a factor of 3, each x-coordinate of the parent function will be multiplied by 3. So for the points:
- \( (0, 0) \) becomes \( (0, 0) \)
- \( (1, 1) \) becomes \( (3, 1) \)
- \( (2, 4) \) becomes \( (6, 4) \)
- \( (3, 9) \) becomes \( (9, 9) \)

From these transformed points, we can find the corresponding values of \( f(1/3x) \):

1. For \( x = 0 \):
\[
f(1/3 \cdot 0) = f(0) = 0
\]

2. For \( x = 3 \):
\[
f(1/3 \cdot 3) = f(1) = 1
\]

3. For \( x = 6 \):
\[
f(1/3 \cdot 6) = f(2) = 4
\]

4. For \( x = 9 \):
\[
f(1/3 \cdot 9) = f(3) = 9
\]

Now we can complete the table:

\[
\begin{array}{|c|c|}
\hline
x & f(1/3x) \\
\hline
0 & 0 \\
3 & 1 \\
6 & 4 \\
9 & 9 \\
\hline
\end{array}
\]

The completed points are \( (6, 4) \) and \( (9, 9) \).
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