Rational Functions

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 an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

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

To find the horizontal asymptote, compare the degrees of the numerator and denominator polynomials.

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 removable discontinuity?

Back

A removable discontinuity occurs at a point where a function is not defined, but can be 'fixed' by redefining the function at that point.

Front

How do you identify a removable discontinuity in a rational function?

Back

A removable discontinuity can be identified by factoring the numerator and denominator and finding common factors.

Front

What is the vertical asymptote of a rational function?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as x approaches a certain value, where the function is undefined.

Front

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

Back

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