Question

Alex says that the function f(x)=(3x)^2 represents a vertical stretch of the quadratic parent function by a factor of 3. Marta says that it represents a horizontal compression by a factor of 1/3. Decide whether one student is correct, both are correct, or neither is correct.

Answer 1

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Answer:

Marta is correct

Explanation:

With respect to parent function g(x), the function g(kx) represents a compression by a factor of 1/k. Here we have k=3, so the function f(x) represents a curve that has distances from the y-axis reduced to 1/3 their parent-function values.

The attached graph shows the horizontal compression.

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If the expression for f(x) were expanded to ...

f(x) = (3x)^2 = 9x^2

we would then recognize it as a vertical stretch of the parent function by a factor of 9. Alex is correct in that the transformation can be interpreted as a vertical stretch, but he is claiming an incorrect stretch factor.