Rational and Radical Functions

Description

A rational function can be written as a fraction with a polynomial in its numerator and denominator. The most basic rational function is the reciprocal function, $f(x)=\frac{1}{x}$. Some rational functions can be graphed as transformations of the parent reciprocal function. Characteristics of the graphs of rational functions include holes, vertical asymptotes, and horizontal asymptotes.

Radical functions include a polynomial expression inside of a radical, such as a square root or cube root. They have an inverse relationship with power functions. Radical functions can be graphed by transforming radical parent functions and by using technology. Rational and radical equations can be solved by algebraic methods or by graphing.

At A Glance

• The reciprocal function $f(x)=\frac{1}{x}$ is the parent function of a family of rational functions.
• Inverse, joint, and combined variation functions show relationships between two or more variables.
• Some rational functions can be graphed as transformations of the parent reciprocal function.
• Holes or vertical asymptotes of a rational function occur when its denominator equals zero. Horizontal asymptotes of a rational function are determined by the end behavior.
• Rational functions can be graphed by identifying their vertical asymptotes, horizontal asymptotes, and holes.
• Radical functions have an inverse relationship with power functions.
• Radical functions are graphed using a variety of techniques, including transformations of the radical parent functions and technology.
• Rational equations can be solved by algebraic methods or by graphing.
• Radical equations can be solved by algebraic methods or by graphing.