Graphing and Solving Rational Equations

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator is zero.

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur at the values of x that make the denominator of a rational function equal to zero.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches infinity or negative infinity.

Front

How do you determine the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator.

Front

What does it mean if a rational function has no horizontal asymptote?

Back

If a rational function has no horizontal asymptote, it means that the function's values increase or decrease without bound as x approaches infinity.

Front

What is the process for solving a rational equation?

Back

To solve a rational equation, first find a common denominator, then multiply both sides by that denominator to eliminate the fractions.

Front

What is a hole in a graph of a rational function?

Back

A hole occurs in the graph of a rational function at x-values that make both the numerator and denominator zero.

Front

How do you identify the x-intercepts of a rational function?

Back

The x-intercepts are found by setting the numerator equal to zero and solving for x.

Front

What is the significance of the y-intercept in a rational function?

Back

The y-intercept is the value of the function when x=0, found by evaluating the function at x=0.