How do you graph a rational function?

Process for Graphing a Rational Function

1. Find the intercepts, if there are any.
2. Find the vertical asymptotes by setting the denominator equal to zero and solving.
3. Find the horizontal asymptote, if it exists, using the fact above.
4. The vertical asymptotes will divide the number line into regions.
5. Sketch the graph.

What is the importance of graphing rational functions?

In this section we will learn about the graphs of rational functions. It is important to be able to find the asymptotes of a rational function in order to graph it. In particular, asymptotes can be used as a guide to sketch the graphs rational functions.

What do you need to graph a rational function?

To graph a rational function, we first find the vertical and horizontal asymptotes and the x and y-intercepts.

What does the numerator of a rational function reveal?

Previously we saw that the numerator of a rational function reveals the x x -intercepts of the graph, whereas the denominator reveals the vertical asymptotes of the graph. As with polynomials, factors of the numerator may have integer powers greater than one.

When does a graph head toward positive infinity?

\\displaystyle x=-1 x = −1 was squared, so we know the behavior will be the same on both sides of the asymptote. The graph heads toward positive infinity as the inputs approach the asymptote on the right, so the graph will head toward positive infinity on the left as well.

Can a rational function be written in factored form?

A rational function written in factored form will have an x -intercept where each factor of the numerator is equal to zero. (An exception occurs in the case of a removable discontinuity.) As a result, we can form a numerator of a function whose graph will pass through a set of x -intercepts by introducing a corresponding set of factors.