Sketch the graph of h(x)=x^2-3x-4/x-4. Label any important features. State the domain and range.

Question

justcatx3 · Answer

Ok, so I already figured out the domain. Set x - 4 to equal zero.

x - 4 = 0
x - 4 + 4 = 0 + 4
x = 4

{x|x =/= 4}

However, I'm unsure how to find the range. I also put the equation in a graphing calculator and found the line to be straight. So I'm not sure what label any important features might mean. I know it doesn't have any extremem values since the line is  straight.

jhonyy9 · Answer

x^2 -3x-4 = (x-4)(x+1)

justcatx3 · Answer

Slightly confused xD Are you saying I should factor it?

justcatx3 · Answer

@thesmartone

mathmale · Answer

Yes, jhonny is suggesting you factor the numerator.  If you do that, you see that x-4 in numerator and denominator can be cancelled out.  Even so, this does NOT mean that x=4 is an acceptable input; it is not.

justcatx3 · Answer

Thank you for explaining~ So that would leave me with x+1. What is this helping me find though? The range?