Question

sketch the graph of each rational function
y=x+2/(x+3)(x-4)

Answer 1

Is it
\[y=\frac{x+2}{(x+3)(x-4)}?\]

Answer 2

yes

Answer 3

Ok that will be a reciprocal graph, with 2 asymptotes

Answer 4

Do you know what are the asymptotes?

Answer 5

would they be -3 and +4

Answer 6

Correct, now we'll find the x-intercept of the graph, do you know how to find it?

Answer 7

no

Answer 8

We'll x-intercept means 'y' must be zero right?

Answer 9

So when
\[y=\frac{x+2}{(x+3)(x-4)} \\ \\ 0=\frac{x+2}{(x+3)(x-4)} \\ \\ 0=x+2 \\ \\ x=-2\]

Answer 10

Intercept at x=-2

Answer 11

ok

Answer 12

The graph will look like