Question

Help me find an equation of a graph!

Answer 1

This is da graph

Answer 2

remember things are formatted (x,y) so the y in the y intercept thing they said is 0.2 the y intercept is also the f(x)= mx+b this is equation for a slop which it looks like its sloping so i would say f(x)=0x+.2 maybe but check with @bibby

Answer 3

Thanks man :D @Sparklestaraa

Answer 4

hey hey wait xd I'm not 110% sure so let me call for reference @ganeshie8

Answer 5

@dan815 come here to play

Answer 6

@Zale101 @mathmate @Marki @ganeshie8

Answer 7

It's not a piece of cake, right? since asymptote are \(\pm 2\), the denominator of the function must be (x+2)(x-2). But, how to define the numerator?

Answer 8

@freckles @satellite73

Answer 9

Definitely not a piece of cake!

@OOOPS had identified the vertical asymptotes as x=\(\pm 2\).
So we start with that. How do we know if we're on the right track? A graphics calculator would be of great help...if you have one.
I prefer the computer, try
https://www.desmos.com/calculator
You only have to type in the equation and poof comes the plot.
\(\color{red}{Warning:~this~tool~will~develop~dependence,~use~with~caution.}\)

So using OOOPS's suggestion as a guide, plot
\(f(x)=\dfrac{1}{(x-2)(x+2)}\)
It's not quite right. At x=2, the graph should both go upwards at x near 2.
That means it calls for \((x-2)^2\)!
Let try that!
\(f(x)=\dfrac{1}{(x-2)^2(x+2)}\)
That's a lot better! mmm, ... not quite.
The middle portion is supposed to plunge down to y=0 at x=1, and our f(x) does not.
Since it just graces (is tangent to) the x-axis, we see that it is a double-root. Let throw in (x-1)^2, but this time at the top (numerator).
Now we have
\(f(x)=\dfrac{(x-1)^2}{(x-2)(x+2)}\)
Plot it and WOW, it looks perfect!
Are we done? Hmmm... remember the question said the y-intercept should be 0.2?
This will take a multiplier "a" of the appropriate value. This will stretch (a>1) or compress (a<1) the graph so that f(0)=0.2.
I'll leave this to you to finish the job!

Answer 10

Here what f(x) looks like before the last step of finding multiplier a.

Answer 11

was i right at all xd

Answer 12

@mathmate My hat off to you. :)

Answer 13

Thank you @OOOPS @Sparklestaraa @mathmate Really helped allot XD

Answer 14

Wow... genius!!