Question

Question 4: Describe the effect of the following transformations in words and then make asketch of the new graph:-1/2f(x – 3) - 4

Answer 1

For this case we need to describe the following transformation given:

$-\frac{1}{2}f(x-3)-4$

Let's take an example and look what happens. We can assume that our function is:

$f(x)=x^2$

If we apply the first part of the transformation we got:

$f(x-3)=(x-3)^2$

And for the total transformation we got:

$-\frac{1}{2}f(x-3)-4=-\frac{1}{2}(x-3)^2-4$

And as we can see our new function have a translation to the right of 3 units and 4 units down.

Since for this case we have a -1/2 at the begin of the equation we have the function rotated around the x axis