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

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.