Rational Expressions and Equations

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 vertical asymptotes of a rational function?

Back

Vertical asymptotes occur where the denominator is equal to zero, provided the numerator is not also zero at those points.

Front

What is a horizontal asymptote?

Back

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

Front

How do you multiply rational expressions?

Back

To multiply rational expressions, multiply the numerators together and the denominators together, then simplify if possible.

Front

What is the process for dividing rational expressions?

Back

To divide rational expressions, multiply by the reciprocal of the divisor and simplify.

Front

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

Back

A rational expression is simplified when there are no common factors in the numerator and denominator.

Front

How do you identify the domain of a rational expression?

Back

The domain of a rational expression includes all real numbers except those that make the denominator zero.

Front

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

Back

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

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity occurs when a factor cancels out, while a non-removable discontinuity occurs where the function is undefined.

Front

How do you graph a rational function?

Back

To graph a rational function, identify asymptotes, intercepts, and test points to understand the behavior of the function.