Unit 8 Rationals 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 hole in a rational function?

Back

A hole occurs in a rational function at a value of x where both the numerator and denominator are zero, indicating that the function is undefined at that point.

Front

How do you find the Least Common Denominator (LCD) of rational expressions?

Back

To find the LCD, factor each denominator and take the highest power of each factor that appears in any of the denominators.

Front

What is end behavior in the context of rational functions?

Back

End behavior describes how the values of a function behave as x approaches positive or negative infinity.

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

To find the horizontal asymptote, 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 vertical asymptote?

Back

A vertical asymptote is a vertical line where a function approaches infinity or negative infinity, typically occurring at values of x that make the denominator zero.

Front

How do you find vertical asymptotes in a rational function?

Back

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

Front

What does it mean for a function to be undefined?

Back

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

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient affects the end behavior of the function and helps determine the horizontal asymptote.