Rational Functions Characteristics

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

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

Back

Set the denominator equal to zero and solve for x.

Front

What is the domain of a rational function?

Back

The domain consists of all real numbers except where the denominator is 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 positive or negative infinity.

Front

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

Back

Compare the degrees of the numerator and denominator polynomials.

Front

What is the x-intercept of a rational function?

Back

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

Front

What is the y-intercept of 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 does it mean if a rational function has a hole?

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 significance of factoring a rational function?

Back

Factoring helps identify vertical asymptotes, holes, and x-intercepts.

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.