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# How do I graph a rational function?

I am extremely frustrated and have been trying for hours..

y=1/x+3

The Vertical Asymptote is -3.

The Horizontal Asymptote is 0.

I have no idea how do get the other graph and the calculators are useless because I dont get how

### 2 Answers

- husoskiLv 74 years ago
One way is to know what the graph of y = 1/x looks like, then realize that y = 1/(x + 3) simply translates that left by 3 units.

When you really don't know what the function looks like, the best way to get an idea is to make a data table (also called a "T chart") of (x,y) pairs on the curve, and the plot those points as dots on the graph. When you have enough points, then sketch the curve(s) connecting them. At least 3 points between any two vertical asymptotes are a good idea...one near the middle of the "gap", and two others closer to the asymptotes on either side.

Save wear on your brain and calculator keys by picking values that are easy to calculate. In your example, with f(x) = 1/(x + 3),

f(-2) = 1/1 = 1 ..... so (-2,1) is on the graph

f(-2.5) = 1/0.5 = 2, so (-2.5, 2) is too

f(-1) = 1/2 .... and (-1, 0.5) is too,

Add (-2.75, 4) and (1, 1/4) and you'll start to see part of a hyperbola forming above y=0 and to the right of x=-3.

Do the same with (-3,25, -4), (-3,5, -2), (-4, -1), (-5, -1/2), (-7, -1/4) and see the other half of the hyperbola,

- ?Lv 74 years ago
If you mean y=1/x + 3, then vertical asymptote is the line x=0, and horizontal asymptote is y = 3.

If you mean y=1/(x+3), then vertical asymptote is the line x=-3, and horizontal asymptote is y=0.

You find vertical asymptotes by looking at where denominator is 0.

You find horizontal asymptotes by asking what happens if x gets large.

You can see a graph of y=1/(x+3) here: