Module E Assessment of Rational Expressions

Front

What is the domain of a rational expression?

Back

The domain of a rational expression is the set of all real numbers except those that make the denominator equal to zero.

Front

What is the range of a rational expression?

Back

The range of a rational expression is the set of all real numbers except those that the function cannot output, often determined by vertical asymptotes.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity as x approaches a.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that the function approaches as x approaches infinity or negative infinity.

Front

How do you find the vertical asymptotes of a rational function?

Back

Set the denominator equal to zero and solve for x.

Front

What is a hole in a graph of a rational function?

Back

A hole occurs at a value of x that makes both the numerator and denominator equal to zero, indicating a removable discontinuity.

Front

How do you simplify a rational expression?

Back

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

Front

What does it mean for a rational expression to be undefined?

Back

A rational expression is undefined when its denominator equals zero.

Front

What is the significance of the numerator in a rational expression?

Back

The numerator determines the values of the function and can affect the range.

Front

What is the significance of the denominator in a rational expression?

Back

The denominator determines the domain and can create vertical asymptotes.