Unit 5.4 Skills Check: Graphing 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 a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur at values of x that make the denominator of a rational function equal to zero, provided those values do not cancel with the numerator.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line y = b that the graph of a function approaches as x approaches infinity or negative infinity.

Front

How do you determine horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator: If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What is a hole in a rational function?

Back

A hole occurs in the graph of a rational function at a value of x where a factor in the numerator and denominator cancels out.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator equals zero, as division by zero is not possible.

Front

What is the significance of excluded values in rational functions?

Back

Excluded values are the x-values that make the denominator zero, indicating where the function is undefined.

Front

How do you graph a rational function?

Back

To graph a rational function, identify vertical and horizontal asymptotes, holes, and plot points to understand the behavior of the function.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.