12/10 Graphing Rational Functions Check

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where a function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes are found by setting the denominator of the rational function equal to zero and solving for x.

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

How do you identify holes in a rational function?

Back

To identify holes, factor both the numerator and denominator, and find common factors that can be canceled.

Front

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

Back

The x-intercept is the point where the graph of the function crosses the x-axis, found by setting the numerator equal to zero.

Front

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

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

Front

What is the end behavior of a rational function?

Back

The end behavior describes how the function behaves as x approaches positive or negative infinity, often determined by the degrees of the numerator and denominator.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity occurs at a hole, while a non-removable discontinuity occurs at a vertical asymptote.

Front

How do you graph a rational function?

Back

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