Question

Graphing this equation: (x^2 -16) / (x^2 -4x)

Can I just choose random x values and substitute them into the equation so I can now how the graph will be?

Answer 1

First try to simplify the equation. I will give you a hint... the numerator can be factored

Answer 2

You could, but not so random would be a better idea.

Answer 3

ok so factorize the numerator...it gives me (x+4)/ (x)
and for the factors, I can choose like -3,-2,-1,0,1,2,3

Answer 4

em I right?

Answer 5

x might be 4...

Answer 6

if i was going to graph
\[y=\frac{x+4}{x}\] i would first identify horizontal asymptote, vertical asymptote and then plot maybe two points

Answer 7

and don't forget to put a big fat hole at (4, 2)

Answer 8

do you know how to identify horizontal and vertical asmptotes?

Answer 9

first, I'd plug in some simple values, like 0 to see where it crosses the X-axis, then solve for 0=(x+4)/x for y-intercept.

Answer 10

asymptotes is the word i am looking for

Answer 11

You get all that?

Answer 12

yes, I know how to identify asymptotes :)

Answer 13

Just to be pedantic, in your question you have no equation, just an expression.

Answer 14

okay, thanks for the correction!
:)

Answer 15

what a nice picture. horizontal asymptote at y = 1, vertical at x = 0 and there you have it. but don't forget that giant hole at (4,2)
\ http://www.wolframalpha.com/input/?i=y%3D%28x%2B4%29%2Fx

Answer 16

So, getting back to your earlier question, you can see now that a less random approach is better and you would want to go beyond 3, -3 to see what is going on.

Answer 17

yes