Question

y=3f(x) when x intercepts are -5 and 3

Answer 1

Answer:

If you know the slope and the y-intercept, then you know all you need to put the f(x) into slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept). In this case, you have f(x)=2x-2.

To go from there to 3f(x-2)-3, your first step should be to get the f(x-2) out of there. To do that, just put in x-2 everywhere the original function has x:

If f(x)=2x-2, then f(x-2)=2(x-2)-2, which simplifies to f(x-2)=2x-6.

Once you’ve got that, substitute and simplify:

\begin{align*}&3f(x-2)-3\\=&3(2x-6)-3\\=&6x-18-3\\&=6x-21\end{align*}

That’s in mx + b form, so the y-intercept is –21.