Thread: Graph of a rational function

How would I graph the following rational function with the following properties?

• f is defined for all real numbers except 3 and -3
• f is an even function
• f(1) = 0, and f(0) = -3/2
• as x -> infinity, f(x) -> 2
• as x -> 3^-, f(x) -> infinity, and as x -> 3^+, f(x) -> -infinity

Any help would be appreciated, thanks!

- You have a vertical asymptote at x=-3 and one at x=3.
- An even function is symmetric with respect to y-axis.
- You probably know how to plot points.
- There is an asymptote at x = 2 the function may or may not cross it but we must see that y goes to 2 as x goes to infinity.
- On the left of x = 3 asymptote, y goes to infinity and on the left it comes from -infinity.
- Because of symmetry, it is the opposite for x = -3 asymptote.