A radical function is made up of a radical expression with the independent variable as the radicand. Radical functions require you to consider the domain of the function before you graph it. The domain is the x values of a given function or relation.

The graph of f(x) = $\sqrt{x- a} + b$ can be obtained by translating the graph of f(x) = $\sqrt{x}$ to A units to the right and then B units up.

## Example 1:

Graph the function f(x) = $\sqrt{x- 1} + 2$ from its parent graph y = $\sqrt{x}$.

Step1:

Plot the graph for y = $\sqrt{x}$.

Step2:

Move the graph by 1 unit to plot the y = $\sqrt{x- 1}$. Then move the graph by 2 units up to draw $\sqrt{x- 1} + 2$.

The domain of the function

y = $\sqrt{x- 1} + 2$ is ≥ 1.

The range of the function

y = $\sqrt{x- 1} + 2$ is ≥ 2.

## Example 2:

What is the domain of the function

y = $\sqrt{x^2 - 10}$?

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Solution:

$x^2$ - 10 ≥ 0

= $x^2$ ≥ 10

-$\sqrt{10}$ and $\sqrt{10}$ are the critical points.

Test x = 0 to see that the interval between -$\sqrt{10}$ and $\sqrt{10}$ doesn’t satisfy the equation.

Answer: The domain of the function f(x) = $\sqrt{x^2 - 10}$ is x ≥ 10 and x ≤ -10.