Question

Sketch the graph of the rational function

5x
---
(x-1)(x+5)

Answer 1

someone please help me

Answer 2

\[\frac{5x}{(x-1)(x+5)}\]?

Answer 3

yes thats the equation

Answer 4

You'll want to label any zeros, holes, vertical asymptotes, horizontal asymptotes, vertical asymptotes, and oblique (skew) asymptotes of your function as the first step. Here's a page that'll explain how to uncover those:
https://people.richland.edu/james/lecture/m116/polynomials/rational.html

To actually draw it, plot test points strategically (choose an \(x\) on either side of zero/asymptote and figure out if the function is positive or negative there) to determine where your curve actually lies relative to the x-axis and its asymptotes.

Answer 5

Also, if you pay attention to the multiplicities of your zeros and poles (vertical asymptotes), then you'll need fewer test points to get an accurate sketch.

Answer 6

the thing thats throwing me off on this question is that the top is 5x so its making x=0 making the whole top 0

Answer 7

can you try drawing one out to help me because im completely lost

Answer 8

Well, if the numerator is 0, as long as the denominator is also not 0, then the value is 0. Otherwise it's undefined.

Answer 9

this is a function of x. You're absolutely correct in saying that it's zero when x is zero, but this isn't an issue. Here's an example:
http://en.wikipedia.org/wiki/Rational_function#Examples

Answer 10

so is it going to be like that for the vertical and how would you find the horizontal?

Answer 11

is it like if the denominator value of x is higher there is no horizontal asymptote

Answer 12

The horizontal asymptotes are the values that the function tend toward when \(x\) becomes large. Try putting in a relatively simple large number and seeing what happens (I recommend \(x=\)10\(^{10}\)).

Answer 13

i thought in order to find the horizontal asymptote you have to look at the degrees of the x? im really confused about how to sketch this one

Answer 14

@numnum you can do it either way.

Answer 15

What I'm suggesting is the same thing, but less formulaic. If you want to use the rules for degrees, that's fine too.

Answer 16

but if i do the degrees then the bottom one is higher then the top meaning there are no horizontal asymptotes?

Answer 17

See, that's why I recommended the other way.

Answer 18

how would you sketch this graph

Answer 19

5x/(x-1)(x+5)

Answer 20

I'd find the horizontal asymptote, check the function's value at 1/5, and use multiplicities to figure out where I'm drawing curves.

Answer 21

Really only the sign of it at 1/5, though.

Answer 22

can you draw out how your going to sketch the graph please

Answer 23

i know for the vertical asymptotes it will be on 1 and -5

Answer 24

No, sorry. Here's a wonderful list of steps, though:
http://www.mathjoys.com/math2/handout/rational.pdf