Question

Find the vertical asymptotes, holes, intercepts, end behavior, and graph for the function y= x(x-1) / x^2-1.

Answer 1

There'd be less ambiguity here if you'd please enclose the denominator "x^2-1" inside parentheses. Want to emphasize that the numerator, x(x-1), is divided by all of "x^2-1."

You will be asked repeatedly to find asymptotes, intercepts, end behavior, etc., so it'd be worth the investment of your time and effort to learn these now.

Hint #1: a VERTICAL INTERCEPT is found by letting x=0. If the function is defined at x=0, the numeric value that results is the y-coordinate of the y-intercept (or vertical intercept).

Answer 2

What specifically do you need to know to complete this problem?

Answer 3

Ok, so to find the y intercept: y= x(x-1) / (x^2-1)
y= (0) / (-1)
y=0
How do I find the x intercept? Is it zero because thats the only value to make it zero?
How do I know where is the vertical asymptote?
I know the domain is x cannot equal 1, and -1
I think the hole is at x=1 because it can cancel on the top and bottom
Um end behavior is y=1?
And how to graph based on this?