Graphs of Rational functions

Front

What is the domain of a rational function?

Back

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

Front

What is the range of a rational function?

Back

The range of a rational function is the set of all possible output values (y-values) that the function can produce.

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 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 at a value of x where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote describes the behavior of the function as x approaches infinity or negative infinity, determined by the degrees of the numerator and denominator.

Front

How do you determine the end behavior of a rational function?

Back

The end behavior can be determined by analyzing the leading coefficients and degrees of the numerator and denominator.

Front

What transformations can be applied to the parent function of a rational function?

Back

Transformations include translations (up, down, left, right), reflections (over the x-axis or y-axis), and stretches or compressions.

Front

What is the parent function of a rational function?

Back

Front

How do you graph a rational function?

Back

To graph a rational function, identify the domain, range, asymptotes, intercepts, and plot points to understand the function's behavior.

Front

What is the significance of intercepts in a rational function?

Back

Intercepts (x-intercepts and y-intercepts) indicate where the graph crosses the axes, providing key points for graphing.