Question

Describe the transformation of f(x)= x2 represented by g. Then graph each function.

Answer 1

There are two tranformations goinf from f(x) to g(x)

Frist, there is a reflection with respect to the x-axis, which is done by changing the sign of the whole function:

$f_1(x)=-f(x)=-x^2$

Next, to get to g(x), ther is a vertical compression of 2, which is done by dividing the whole function by 2:

$g(x)=\frac{f_1\mleft(x\mright)}{2}=-\frac{1}{2}x^2$

So, to graph it, we can start from f(x):

$f(x)=x^2$

Then reflect and compress like we have done.

We get the function og g(x):

$g(x)=-\frac{1}{2}x^2$