Consider the function f(x) = x2-x-12/x-4 . Describe the graph of this function. Include all discontinuities, intercepts, and the basic shape of the graph.

Question

mathmate · Answer

Consider the expression: (x^2-x-12)/(x-4)=(x-4)(x+3)/(x-4) =(x-3) after cancelling the common factor for points where x not equal to 3. At x=3, the function is undefined. Is that enough to get you gonig?

anonymous · Answer

You can't cancel and forget about the x-4 term.  There's still a point discontinuity there.

anonymous · Answer

But otherwise it behaves like the line.

anonymous · Answer

now im really confused @mathmate @vf321

mathmate · Answer

Sorry, I meant to say that the function is undefined at x=4 (where we cancelled).
The remaining points behave like y=x+3.

anonymous · Answer

@raytiller1 What mathmate's saying is right - If you notice,
$$f(x)=\frac{x^2-x-12}{x-4} = \frac{(x-4)(x+3)}{x-4}$$
So, when x!=4, you have some number x-4 on the numerator and in the denominator, so they cancel.
$$x \neq 4::f(x) = \frac{x-4}{x-4}(x+3)=1(x+3)$$
When x does equal 4, you get 0/0, a discontinuity.

anonymous · Answer

thanks guys @vf321 @mathmate

mathmate · Answer

You're welcome!   :)