Question

Predict what would happen to the grap when it went from y=f(x)/g(x) to y= g(x)/f(x), when f(x)=x+1 and g(x)=1 -x^2

Answer 1

We are given that f(x)=x+1 and g(x)=1-x^2.

First, consider that

$g(x)=(1\text{ -x)(x+1)}$

so, we have that

$\frac{f(x)}{g(x)}=\frac{x+1}{(1\text{ -x)(x+1)}}$

so, whenever x is not -1, we get

$\frac{f(x)}{g(x)}=\frac{1}{1\text{ -x}}=\text{ -}\frac{1}{x\text{ -1}}$

whose graph is like this

however, note that

$\frac{g(x)}{f(x)}=\frac{(1\text{ -x)(x+1)}}{(x+1)}$

so, whenever x is not -1 we have

$\frac{g(x)}{f(x)}=\text{ -(x -1)}$

whose graph looks like this