# Roots and Radicals

## Use Radicals in Functions


### Evaluate a Radical Function

In this section we will extend our previous work with functions to include radicals. If a function is defined by a radical expression, we call it a radical function.
The square root function is 
The cube root function is 
To evaluate a radical function, we find the value of f(x) for a given value of x just as we did in our previous work with functions.
We follow the same procedure to evaluate cube roots.
The next example has fourth roots.

### Find the Domain of a Radical Function

To find the domain and range of radical functions, we use our properties of radicals. For a radical with an even index, we said the radicand had to be greater than or equal to zero as even roots of negative numbers are not real numbers. For an odd index, the radicand can be any real number. We restate the properties here for reference.
So, to find the domain of a radical function with even index, we set the radicand to be greater than or equal to zero. For an odd index radical, the radicand can be any real number.
The next example involves a cube root and so will require different thinking.

### Graph Radical Functions

Before we graph any radical function, we first find the domain of the function. For the function,  the index is even, and so the radicand must be greater than or equal to 0.
This tells us the domain is  and we write this in interval notation as 
Previously we used point plotting to graph the function,  We chose x-values, substituted them in and then created a chart. Notice we chose points that are perfect squares in order to make taking the square root easier.
Once we see the graph, we can find the range of the function. The y-values of the function are greater than or equal to zero. The range then is 
In our previous work graphing functions, we graphed  but we did not graph the function  We will do this now in the next example.

### Key Concepts

1. Properties of 


2. Domain of a Radical Function



### Practice Makes Perfect

Evaluate a Radical Function
In the following exercises, evaluate each function.
Find the Domain of a Radical Function
In the following exercises, find the domain of the function and write the domain in interval notation.
Graph Radical Functions
In the following exercises, ⓐ find the domain of the function ⓑ graph the function ⓒ use the graph to determine the range.

### Writing Exercises


### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?