# Graphing function and its reciprocal, also get domain/range

• Jun 7th 2009, 06:34 PM
olen12
Graphing function and its reciprocal, also get domain/range
Hello.

I have the function y=x^2 - 3
Would the reciprocal be: y= 1/(x^2-3)?

(I need to graph these by hand without a graphing calculator.)

Now how would I graph y=x^2-3?
The -3 tells me the min of the range is -3? So I start at -3 and go up, but how do I know how wide to make it or where to make the zeroes?

Same thing for the reciprocal, I have no idea to graph that and find the range/domains of it too.

Any help would be greatly appreciated.
• Jun 7th 2009, 07:33 PM
VonNemo19
Quote:

Originally Posted by olen12
Hello.

I have the function y=x^2 - 3
Would the reciprocal be: y= 1/(x^2-3)?

(I need to graph these by hand without a graphing calculator.)

Now how would I graph y=x^2-3?
The -3 tells me the min of the range is -3? So I start at -3 and go up, but how do I know how wide to make it or where to make the zeroes?

Same thing for the reciprocal, I have no idea to graph that and find the range/domains of it too.

Any help would be greatly appreciated.

The function $\displaystyle y=x^2-3$ is simply the same thing as $\displaystyle y=x^2$, a parabola that has shifted down the y axis three units.
So just graph x^2 and slide it down.

The function $\displaystyle y=\frac{1}{x^2-3}$ is simply a hyperbola. Whenever dealing with hyperbolas, always look for vertical asymptotes. i.e. where the function is undefined. Theses will help you sketch the graph.