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

1 Answer
Jul 26, 2015

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]}