Rational Expression Review

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

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 present in any of the denominators.

Front

What is the domain of a rational expression?

Back

The domain is the set of all real numbers except those that make the denominator zero.

Front

What is a vertical asymptote?

Back

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

Front

What is a horizontal asymptote?

Back

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

Front

Back

Set the denominator equal to zero and solve for x. The domain excludes these x-values.

Front

What does it mean for a rational function to have a hole?

Back

A hole occurs in the graph of a rational function at a value of x that makes both the numerator and denominator zero.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) of a function.

Front

How do you simplify a rational expression?

Back

Factor the numerator and denominator and cancel out any common factors.

Front

What is the significance of the degree of the numerator and denominator in rational functions?

Back

The degree helps determine the behavior of the function, including the presence of horizontal and vertical asymptotes.