Our parent function is f(x)=x^2. A vertical stretch by a factor of k means that every point (x,f(x)), has been transformed into (x,kf(x)). Alex is clearly incorrect as our parent function has been transformed to (x,9f(x)), not (x,3f(x)). A horizontal stretch(or compression) by a factor of k means our function has been transformed to (x/k,f(x)). Here, Marta is saying our function should look like (3x,f(x)). This can also be achieved by plugging 3x into the parent function, which would give us f(3x)=(3x)^2, so it seems that Marta is the correct one.
Answer:
Marta is correct
Step-by-step 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.
