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# Finding the rational function for this graph

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1 I got 2(x-2)/(x+2)(x-4) but when I plugged it in, it wasn't the same graph.

The characteristics I got were

VA: x=-2,4

HA: y=0

x int: 2

y int: 1/2

Nov 10, 2020

#1
+1

You are on the right track

Certainly a part of the denominator must be  (x+2)(x-4)

And given that (2,0) is on the graph, the numerator must have (x-2) in it.

Plus it looks a bit like a parabola, with a double root at x=2  so i suspect the numerator will be squared (I am not so sure that my logic is sound here)

Anyway so far I am thinking that it might be ..

$$y=\frac{k(x-2)^2}{(x+2)(x-4)}\\$$       where k is a constant.

It looks like it might go through (0, 0.4)

when x=0

LHS= 4k / -8 = -k/2

-k/2=0.4

k=-0.8

So maybe it is

$$y=\frac{-0.8(x-2)^2}{(x+2)(x-4)}\\$$

check:

This is certainly not completely correct but the diagram you have provided is not very good.

This is probably close enough.

Maybe  -1 would have looked a little closer than -0.8 .  The the y intercept would have been  0.5 Nov 11, 2020