2.7 Graphs of Rational Functions

g(x)=

First find the x and y intercept. (if any)

y-Intercept: (0,)because g(0)=

x-Intercept: There is none because when you plug in 0 for y its 30

Next we need to find the vertical and horizontal asymptote . (if any)

V.A: Just the denominator so x-2=0 x=2

H.A: Is the trickiest because its going to have 3 different scenarios

1. Powers are the same and you have to divide by leading coefficients.

2. Numerator has a larger power

3.Denominator has a larger power

1. 2. 3.

H.A= H.A= no asymptote H.A=0

So in our situation of

g(x)= when x=1,000,000,000,000 the denominator is going to be much bigger than the numerator so we call it 0.

we have everything we need to graph now.

if all the steps were done right it should come out to this

There are also situations in where we get HOLES in the graph and this occurs when we have the same factor on the numerator and denominator.

g(x)= ,, if we go to zoom decimal we can see the graph is as so

f(x)=

*rule of thumb- if one side is negative probably the other is positive