Intercepts are the points where the graph crosses the x-axis, and zeroes are the values of x that make the function equal to zero. Signup and view all the answers

What does finding the asymptotes of a rational function involve?

Identifying the values of x for which the function approaches positive or negative infinity. Signup and view all the answers

What is an asymptote of a rational function?

A line that the graph of the function approaches but does not touch as x approaches positive or negative infinity. Signup and view all the answers

Study Notes

Asymptotes of a Rational Function

An asymptote of a rational function is a line that the graph approaches as the input (x) increases or decreases without bound, but never reaches.
Finding the asymptotes of a rational function involves determining the values of x that make the denominator equal to zero.

Zeroes of a Rational Function

Finding the zeroes of a rational function involves setting the numerator equal to zero and solving for x.
The zeroes of a rational function are the values of x that make the function equal to zero.

Relationship between Intercepts and Zeroes

The x-intercepts of a rational function are the same as the zeroes of the function.
The y-intercept of a rational function is the value of the function when x is equal to zero.
The intercepts and zeroes of a rational function are related in that they are the points at which the graph of the function crosses the x-axis or y-axis.