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

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

so, whenever x is not -1, we get

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

whose graph is like this

however, note that

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

so, whenever x is not -1 we have

`(g(x))/(f(x))=\text{ -(x -1)}`

whose graph looks like this