Question

How do you compare and contrast the graphs of `y=x-2` and `y=(x^2+5x-14)/(x+7)`?

Answer 1

`"see explanation"`

Explanation:

`"consider "y=(x^2+5x-14)/(x+7)`

`"factorising the numerator gives"`

`y=((x+7)(x-2))/(x+7)`

`"cancelling the factor "(x+7)" from numerator/denominator"`

`y=(cancel((x+7))(x-2))/cancel((x+7))=x-2`

`"the removal of "(x+7)" from the numerator/denominator"`
`"indicates there is a hole at "x=-7`

`rArry=(x^2+5x-14)/(x+7)" reduces to "y=x-2`

`"the graphs of "y=(x^2+5x-14)/(x+7)" and "y=x-2`

`"are the same graph "`

`"the only difference being that "y=(x^2+5x-14)/(x+7)`

`"has a hole at "x=-7" whereas "y=x-2" does not"`