Question

How do you graph `f(x)= (3x^2-7x-6)/(x-3)`?

Answer 1

You draw a straight line through `(0,2)` and `(1,5)`

Explanation:

First, note that yopur function is undefined for `x=3`, since that would make the denominator of the fraction equal to zero.

Next, notice that you can write

`3x^2-7x-6 = (x-3)(3x+2)`

Therefore, `f(x)` is actually equivalent to

`f(x) = (cancel(x-3) * (3x+2))/cancel(x-3) = 3x+2`

This function represents a straight line through points `(0,2)` and `(1,5)`, with the added mention that point `(3,11)` represents a hole in the graph.

graph{(3x^2-7x-6)/(x-3) [-20.64, 19.92, -9.38, 10.91]}