Question

What is the range of the function `f(x)=(x-3)/(x+4)`?

Answer 1

`y inRR,y!=1`

Explanation:

To find the value/s that y cannot be.

`"Rearrange to make x the subject"`

`y=(x-3)/(x+4)`

`color(blue)"cross-multiplying ""gives"`

`y(x+4)=x-3`

`rArrxy+4y=x-3`

`rArrxy-x=-3-4y`

`rArrx(y-1)=-3-4y`

`rArrx=(-3-4y)/(y-1)`

The denominator cannot be zero. Equating the denominator to zero and solving gives the value that y cannot be.

`"solve " y-1=0rArry=1larrcolor(red)" excluded value"`

`"range is " y inRR,y!=1`