Question

Hi, I need to find the x and y intercept of (x^2-16)/(x^2-4x) how do i do this?

Answer 1

I know that for the x-intercept I just equal the equation to 0...but do I need to equal the whole equation, or just the denominator?

Answer 2

As long as the denominator is not zero, you only need to study the numerator.

Answer 3

So you get two equations.

\[y = -16, x^2-4x \neq 0\]

Answer 4

The other one:
\[x^2−16=0,x^2−4x≠0\]

Answer 5

The first one gives you the y intercept and the second one x.

Answer 6

for the y intercept you just plug 0 in as x to the whole equation

Answer 7

which in this case gives you -16/0 which is undefined

Answer 8

ahh but you can simplify the equation first...the top part is the same as (x+4)(x-4)/(x(X-4)) which becomes (x+4)/x

Answer 9

so this crosses the x axis at -4 and never crosses the y axis