Question

How do you graph `y =(x^2+4x-2)/(x^2-x-7)`?

Answer 1

See graph and details.

Explanation:

By actual division,

`y = 1 + ( 5 ( x + 1 ))/(( x - a )(x - b )), a,b = 1/2( 1 +- sqrt29 )`. So,

`( y - 1 )( x - a )( x - b ) = 5 ( x + 1 )`, with the asymptotic

`y ne 1, x ne a and x ne b )`.

See graph, with asymptotes. y = 1, x = a and x = b.
graph{(y(x^2-x-7)-(x^2+4x-2))(y-1)(x-1/2-1/2sqrt29+0.00001y)(x-1/2+1/2sqrt29+0.00001y)=0}