Rational Functions Test

Front

Where does this graph have a hole?

Back

A hole in a rational function occurs at the value of x that makes both the numerator and denominator equal to zero after factoring. For example, if the function is (x-5)(x+4)/(x-5)(x+3), there is a hole at x=5.

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. For rational functions, it is determined by the degrees of the numerator and denominator.

Front

How to find the vertical asymptote(s)?

Back

Vertical asymptotes occur at the values of x that make the denominator equal to zero, provided that these values do not also make the numerator zero.

Front

When does the horizontal asymptote equal zero?

Back

The horizontal asymptote equals zero when the degree of the numerator is less than the degree of the denominator.

Front

What are asymptotes?

Back

Asymptotes are lines that the graph of a function approaches but never touches. They can be vertical, horizontal, or oblique.

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.

Front

How do you determine the horizontal asymptote for rational functions?

Back

1. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. 2. If the degrees are equal, the horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator. 3. If the degree of the numerator is greater, there is no horizontal asymptote.

Front

What is the significance of a hole in a rational function?

Back

A hole indicates that there is a point on the graph where the function is not defined, typically due to a common factor in the numerator and denominator.

Front

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

Back

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

Front

What is the relationship between the degrees of the numerator and denominator?

Back

The relationship determines the behavior of the function as x approaches infinity and the existence of horizontal asymptotes.