Examples:

A radical as you might remember is something that is under a radical sign e.g. a square root. A radical function contains a radical expression with the independent variable (usually x) in the radicand. Usually radical equations where the radical is a square root is called square root functions.

An example of a radical function would be

y=√x

This is the parent square root function and its graph looks like

If a < 0 the graph

y=a√x

Is the reflection in the x-axis of the graph

y=|a|√x

If we compare this to the square root function

y=a√x

We will notice that the graph stretches or shrinks vertically when we vary a

|a|>0 ⇒ vertical. stretch

0<|a|<1 ⇒ vertical shrink

In the graph below we have radical functions with different values of a

Another square root equation would be

y=a√x-b +c

If you look at the graphs above which all have c = 0 you can see that they all have a range ≥ 0 (all of the graphs start at x=0 since there are no real solutions to the square root of a negative number). If you have a c ≠ 0 you'll have a radical function that starts in (0, c). An example of this can be seen in the graph to the left

The value of b tells us where the domain of the radical function begins. Again if you look at the parent function it has a b = 0 and thus begin in (0, 0) If you have a b ≠ 0 then the radical function starts in (b, 0).

If both b ≠ 0 and c ≠ 0 then the radical function starts in (b, c)