I'm not sure why I cannot comprehend this, maybe someone could give me some insight?

y=f(x) gives x-intercepts of -6 and -4. (all questions are based from this given information.)

So far they have asked me to find x-intercepts for y=f(x+7) which are -13 and -11.
as well as x-intercepts for y=f(x-9) which are 3 and 5

But the next part asks me for x-intercepts of y=2f(x).

It seems simple and I should know this.

An explanation would help much more than just an answer, thanks.

This post was edited by Iffy00 on Jan 25 2015 07:18pm

the x axis is where the function meets y = 0. if you double y, it's still 0. so the x intercepts are the same.

the intercepts would be again -6,-4

say f(x) looks sumthin like
f(x) = (x+6)(x+4)
then

f(x+7) = ((x+7) + 6)((x+7)+4)
f(x+7) = (x+13)(x+11)
this is the resaon the intercepts for f(x+7) is -13,-11

now 2f(x) = 2(x+6)(x+4)
wich dos not change the intecepts

Thanks for the explanation, so intercepts won't change, just the picture of the function, interesting.
Too simple for me to comprehend.

The final part was y=f(-x) which is just the reflection on y-axis so answer would be 6 and 4.

This post was edited by Iffy00 on Jan 25 2015 07:37pm

To generalize, suppose that you know that the function
a * f( g(x) )
has zeroes at say x = -6 and x = -4.
then, solve the equation g(x) = -6 for x, and solve g(x) = -4 for x to find the zeroes of the equation above.

so if 2f(x^2) had a zero at 9 then you know f(x) has zeroes at 3 and -3.