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Vertically compress by a factor of 1/3 Y=9(5)^x arrow symbolQuestion
Vertically compress by a factor of 1/3
Y=4(x+2)^2 arrow symbol
Y=4(x+2)^2 arrow symbol
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Answered by
GPT-4o mini
To apply a vertical compression by a factor of \( \frac{1}{3} \) to the function \( y = 4(x + 2)^2 \), you need to multiply the entire function by \( \frac{1}{3} \).
Starting with:
\[ y = 4(x + 2)^2 \]
To compress it vertically by a factor of \( \frac{1}{3} \), you would do:
\[ y = \frac{1}{3} \cdot 4(x + 2)^2 \]
This simplifies to:
\[ y = \frac{4}{3}(x + 2)^2 \]
So, the new function after the vertical compression by a factor of \( \frac{1}{3} \) is:
\[ y = \frac{4}{3}(x + 2)^2 \]
Starting with:
\[ y = 4(x + 2)^2 \]
To compress it vertically by a factor of \( \frac{1}{3} \), you would do:
\[ y = \frac{1}{3} \cdot 4(x + 2)^2 \]
This simplifies to:
\[ y = \frac{4}{3}(x + 2)^2 \]
So, the new function after the vertical compression by a factor of \( \frac{1}{3} \) is:
\[ y = \frac{4}{3}(x + 2)^2 \]