Rational Function Graphs Review

Front

What is a rational function?

Back

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 of a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator zero, provided that these values do not also make the numerator zero.

Front

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

Back

A hole occurs in the graph of a rational function at a value of x that makes both the numerator and denominator zero, indicating a removable discontinuity.

Front

How do you find 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 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 intervals of increase or decrease for a rational function?

Back

To determine intervals of increase or decrease, analyze the first derivative of the function. If the derivative is positive, the function is increasing; if negative, it is decreasing.

Front

What is the significance of the degree of the numerator and denominator in rational functions?

Back

The degree of the numerator and denominator helps determine the behavior of the function at infinity and the existence of horizontal asymptotes.

Front

What is the process for graphing a rational function?

Back

1. Identify the domain. 2. Find x-intercepts and y-intercepts. 3. Determine vertical and horizontal asymptotes. 4. Analyze intervals of increase/decrease. 5. Sketch the graph.

Front

What is the y-intercept of a rational function?

Back

The y-intercept is found by evaluating the function at x=0, provided that the function is defined at that point.