Question

Can someone please help me graph this rational function: 2
----------
x^2-2x-3
Also need the
Domain:
x and y intercepts:
horizontal asymptotes:
vertical asymptotes:

*This is a practice problem, if someone can help me find the answers to this problem i can help myself do the actual problem that i need.
Thanks!

Answer 1

\[y = \frac{2}{x^2 - 2x - 3}\]

Answer 2

First factor the denominator

\[y = \frac{2}{(x - 3)(x + 1)}\]

Answer 3

Okay

Answer 4

Next, figure out the asymptotes.

We know \(x \ne 3\) and \(x \ne 1\)

Answer 5

So the vertical asymptotes would be x=3 , x=-1?

Answer 6

The way to know if those are asymptotes is to test numbers very close such x = 2.9 and x = 3.1

if they diverge, meaning if one is negative and the other is positive, then it is safe to assume that x = 3 is an asymptote. Same goes for x = -1

Answer 7

If you know how to program your calculator, you can program the function into the calculator to test such points.

Answer 8

Okay, so vertical asymptotes are x=3 and x=-1. Now how about the rest?

Answer 9

Okay, yes, they are both asymptotes, so we can plot those.

Answer 10

To find the horizontal asymptotes, we have to figure out what number we can input into y such that we cannot solve for x.

Answer 11

There's one obvious number that would work.

Answer 12

0?

Answer 13

Yes, very good. We at least know that it is not part of the graph.

Answer 14

There's no other number that will work

Answer 15

Okay, so the horizontal asymptote is y=0?

Answer 16

Let's try to find some intercepts.

Answer 17

What happens if x = 0?

Answer 18

Ive already tried, are these correct.
x intercept, x= (0, -2/5) y intercept, (2,0) ?

Answer 19

For the y intercept, you insert x = 0, then solve for y

Answer 20

For the x intercept, you insert y = 0, then try to solve for x. We already tried this and we didn't get anywhere, so we can assume there is no x intercept.

Answer 21

But there is a y-intercept

Answer 22

So the x intercept is 0? whats the y intercept?

Answer 23

You are confused. I never said what any intercept is.

Answer 24

What I posted were the steps to find the intercepts.

Answer 25

y-intercept means that we automatically assume x will be zero because in order for a point on the graph to intercept the y-axis, x must be zero. To figure out at what value the point on the graph intercepts the y-axis, we input x = 0 into the given formula like so:

\[y = \frac{2}{0^2 - 2(0) - 3}\]

Answer 26

Notice that upon doing so, \[y = -\frac{2}{3}\]

Answer 27

Where are you getting -2/5

Answer 28

Do you have a 5 instead of 3 in your original problem?

Answer 29

No, i realized what i was doing wrong. So the y intercept is -2/-3?

Answer 30

I'm shaking my head right now. You've added an extra negative for no reason.

Answer 31

The fraction is negative once. you don't add two negatives to a negative fraction. If you do that, the fraction becomes positive.

Answer 32

\[-\frac{2}{3} \ne \frac{-2}{-3}\]

Answer 33

Sorry, thats what i means, not two negatives.

Answer 34

So the y intercept is (0,-2/3)

Answer 35

Yes

Answer 36

Now, if you've programmed your calculator as I have, all you have to do is just simply plot the points:
f(-7)
f(-6)
f(-5)
f(-4)
f(-3)
f(-2)
f(0)
f(1)
f(2)
f(4)
f(5)
f(6)
f(7)

Answer 37

Is the x intercept 0 or none? and i also need the domain

Answer 38

To find the x intercept, let y = 0 then solve for x. If you are not able to solve for x, then there is no x-intercept.

Answer 39

When you are done, you should get something like this: