Question

A graph has equation y=2x^2-4. What is the equation of the new graph when it is.

(a) Scaled by a factor of 3 parallel to the y-axis
(b) Scaled by a factor of 0.2 parallel to the x-axis.

Answer 1

Hi, I thought I knew how to answer questions on this topic, but a few questions have confused me.

Just to check, (that my background knowledge is right), but f(2x), you stretch by a s.f. of 1/2 parallel to the x axis, and for 2f(x), you stretch by a s.f. of 2 parallel to the y axis? So if they say stretch by a scale factor of 3 in the x axis, and you have to derive the original equation, you just put 1/3x (for x's) right?

Here are just two questions which got me a bit confused:

"The graph of y=1/x^2 is stretched by a factor of 3 in the x direction. Show that the same could be achieved by a stretch in the y direction, and find the factor of the stretch".

So I worked out the eq of the new graph. So it's f(1/3x), so y = 1/ (1/3x^2) and that = 3x^2.

But I'm unable to find a number infront of 1/x^2 to make it 3x^2...and the answer is meant to be 9, but I'm unsure how to get that :/

"The graph y=2x^2 is stretched by a factor of 2 in the y-direction. Find the equation of the new graph. The graph is then stretched by a factor of 3 in the x-direction. Find the equation of the final graph and state clearly how you could achieve the same final result with a) just one stretch in the x direction b) just one stretch in the y-direction."

So I worked out the first graph correctly. You do, 2f(x) so, 2 ( 2x^2) = 4x^2.

Then for the second graph, stretched by a scale factor 3, but for x you do 1 / 3. So f(1/3x). So 4(1/3x)^2 = 4/3x^2.

But the answer is 4/9x^2? As I got that graph wrong, the subsequent answers were wrong too. I'd be grateful for some help!
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