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 \( f(1/3x) \):
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For \( x = 0 \): \[ f(1/3 \cdot 0) = f(0) = 0 \]
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For \( x = 3 \): \[ f(1/3 \cdot 3) = f(1) = 1 \]
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For \( x = 6 \): \[ f(1/3 \cdot 6) = f(2) = 4 \]
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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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