Rational Functions Barry Edit

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 the x-intercept of a function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis, meaning the value of y is zero.

Front

How do you find the x-intercept of a rational function?

Back

To find the x-intercept, set the numerator of the rational function equal to zero and solve 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 positive or negative infinity.

Front

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

Back

The horizontal asymptote can be determined by comparing the degrees of the numerator and denominator polynomials.

Front

What is the significance of vertical asymptotes?

Back

Vertical asymptotes indicate values of x where the function approaches infinity or negative infinity, typically where the denominator is zero.

Front

How do you find vertical asymptotes in a rational function?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Front

What is a hole in a rational function?

Back

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

Front

How do you identify a hole in a rational function?

Back

To identify a hole, factor both the numerator and denominator and look for common factors that cancel out.

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 leading coefficients.