A hyperbola is a function with its equation in the form or .
For example, is a discontinuous curve since the function is undefined at x=0.
Drawing up the table of values gives:
What happens to the graph as x becomes closer to 0?
What happens as x becomes very large in both positive and negative directions?
The value of y is never 0. Why?
To sketch the graph of a hyperbola, we can use the domain and range to help find the asymptotes (lines towards which the curve approaches but never touches.
Use this Geogebra file to explore the hyperbolic function: