Rational Functions Test Review

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 the input approaches a.

Front

How do you find vertical asymptotes of a rational function?

Back

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

Front

What does the term 'domain' refer to in rational functions?

Back

The domain of a rational function is the set of all possible input values (x) for which the function is defined, excluding values that make the denominator zero.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote is a horizontal line that the graph of the function approaches as x approaches infinity or negative infinity.

Front

How do you determine 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 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 of the function crosses the y-axis, found by evaluating the function at x = 0.

Front

Back

Front

What is the difference between removable and non-removable discontinuities?

Back

Removable discontinuities occur when a factor cancels in the numerator and denominator, while non-removable discontinuities occur when the denominator is zero and cannot be canceled.