I am refering to the question posted on Tuesday, June 6, 2017 at 8:26pm.

Question

"how to graph y= (x^2-3x-10)/(x-2)"

This is the reply I got:

Pre-Calculus 12 - Damon, Tuesday, June 6, 2017 at 9:21pm
(x-5)(x+2)/(x-2)

well we know it is 0 at x = 5 and at x = -2
and we know it explodes at x = 2

we know it goes to y = x as x gets +big

we know it goes to y = -x as x gets -big

now between those zeros at -2 and+5
lies x = 0 when y is 10/2 = 5

so that is a start :)

My question is I don't understand what you mean "it is 0 at x=5 and at x=-2"? I haven't been taught how to graph these questions so please help!

Answer 1

y = (x-5)(x+2)/(x-2)

a fraction is zero when its numerator is zero, right?

Damon was just trying to give you the x-intercepts as an aid to graphing the curve.

With Damon's input, you have the x-intercepts, the asymptote, and the y-intercept.

Unfortunately, the asymptote is not y=x or y=-x. If you do the division, you see that

y = x-1 - 12/(x-2)

Now, as x gets huge, 12/(x-2) goes to zero, so the asymptote is the line

y = x-1

See the info at

http://www.wolframalpha.com/input/?i=(x-5)(x%2B2)%2F(x-2)

Answer 2

Are there specific steps to graphing this equation or do you just plot points?

Answer 3

well, you have to know the basic steps to finding intercepts and asymptotes.

Review the examples in your text, and then it's just a matter of figuring out the relevant features of the graph. The intercepts and stuff are just handy landmarks to pinpoint specific places.