We have the expression:
[tex]f(x)=4x^8-6x^2+3x-7[/tex]And the question wants to know how many sign changes we have when we plot -x in the function, to solve this we need to remember that:
[tex](-1)^n=1\text{ when n is even and }(-1)^n=-1\text{ when n is odd}[/tex]So, lets solve:
[tex]f(-x)=4(-x)^8-6(-x)^2+3(-x)-7\rightarrow f(-x)=4x^8-6x^2-3x-7[/tex]So, only the sign of 3 changed, so we have only one change.
