Question

Use the graph below to construct the rational function that it represents. The thicker blue lines represent the graph and the thinner red lines represent the asymptotes. Please show all of your work. (see attached graph) Use the graph below to construct the rational function that it represents. The thicker blue lines represent the graph and the thinner red lines represent the asymptotes. Please show all of your work. (see attached graph) @Mathematics

Answer 1

first guess is f(x) = x / (x^x - 9)

let me check that out

Answer 2

i meant x / (x^2 - 9)

Answer 3

ok. what do you mean by first guess? lol

Answer 4

lol - not sure yet - what do u think?

Answer 5

lol- Im thinking y=x/(x-3)(x+3)...I wonder if Im wrong though. lol

Answer 6

\[\frac{x}{(x-3)(x+3)}=\frac{x}{x^2-9}\]...

Answer 7

mahone- are you sure?

Answer 8

how did you get that answer? Can you show the work please :)

Answer 9

i'm saying what you and jimmyrep said are the same thing...

Answer 10

i'm not answering your question, per se...

Answer 11

oh haha

Answer 12

we are all correct - i just graphed it on my calculator!!

Answer 13

the asymptotes are at x = -3 and x = +3 - the values which make the denominator = 0.
so this gives the (x+3)(x-3) which expands to x^2 - 9
and also x = 0 gives f(x) = 0 so it goes through the origin

Answer 14

also it has horizontal asymptote at y = 0, so you know the degree of the numerator must be less than the degree of the denominator. the fact that it goes through the origin tells you that up top should be an x.

Answer 15

woo hoo, thanks!!