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

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

Back

To find the y-intercept, set x = 0 in the function and solve for y.

Front

What does it mean if a rational function has an undefined y-intercept?

Back

An undefined y-intercept means that the function does not cross the y-axis, often due to a vertical asymptote.

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 a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches but never touches, typically 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 equal to zero and solve for x.

Front

What is the domain of a rational function?

Back

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

Front

What does it mean if a rational function has a hole in its graph?

Back

A hole occurs when a factor in the numerator and denominator cancels out, indicating a point where the function is undefined.

Front

How do you identify the x-intercepts of a rational function?

Back

To find the x-intercepts, set the numerator equal to zero and solve for x.