The graph of a radical function
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 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⇒verticalstretch0<|a|<1⇒verticalshrink
In the graph below we have radical functions with different values of a
If a < 0 the graph
y=a√x
Is the reflection in the x-axis of the graph
y=|a|√x
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 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
y1=√x
y2=3√x
y3=√x+2
y4=√x−1
y5=√x(x−2)+1