### Radical and Power Functions

**radical function**is one whose rule can be written using an expression with a variable under a root, such as a square root or cube root:

### Power Functions and Radicals

Even Power Functions and Radicals | Odd Power Functions and Radicals |
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### Graphing Radical Functions

Radical functions can be difficult to graph by hand. Even when radical functions are graphed using technology, it can be useful to analyze the functions to understand the properties of the graphs.

For some calculators, it may be difficult to enter roots other than square and cube roots. In such cases, it may be necessary to use rational exponents. Taking the $n$th root of an expression is the same as raising it to the power of $\frac{1}{n}$:Look at the expression under the radical. Values of $x$ that make this expression negative are not in the domain of $f$ because the square root of a negative value is not a real number.

Graph the given function together with:Identify the domain and range of $f$.

The domain is $x\leq-1$ and $x\geq5$.

The graph shows that all the $y$-values are on or above the $x$-axis, so the range is $y\geq0$.

Analyze the function. Identify maxima (highest points), minima (lowest points), and zeros. Describe where the function is increasing and decreasing.

The graph shows the minimum value of zero, which occurs at $x=-1$ and $x=5$. There is no maximum.

The zeros of the function are also at $x=-1$ and $x=5$.

The function is decreasing for $x<-1$ and increasing for $x>5$.