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
This is the parent square root function and its graph looks
like
If we compare this to the square root function
We will notice that the graph stretches or shrinks vertically
when we vary a
In the graph below we have radical functions with different
values of a
If a < 0 the graph
Is the reflection in the x-axis of the graph
Another square root equation would be
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
below
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)
Video lesson: Compare the radical functions
