RADICAL FUNCTIONS

First thing to know about radical functions is that it involves a radical with a variable in the radicand.


One major rule to keep in mind is that the x-value in the radicand can be any number, as long as it is not negative. Taking the square, cube, fourth, or any root of a negative number is impossible.

Now let's look at a basic radical function.

y = √x

An important thing to do that people tend to forget is to solve for the inequality. Take the value from inside the radical and equate it to zero.

x = 0

Now simply replace the symbol with the inequality symbol.

x ≥ 0

From that, we know that x has to be greater or equal to zero.

The simplest way to represent this radical function on a graph is to use a table of values. There are other methods, such as comparing graphs and solving the equation, but table of values seem to be the easiest method. To make it even easier for yourself, you should pick values for x that you can take the square root out of.

Examples: Values of 0, 1, 4, 9, and 16




 
Irrational numbers such as 3, 5, 6, 7 and so on can also be chosen as the x-value, but the result will turn out with decimals, making it harder for yourself to graph.










Now comes the graphing. Simply plot these points down.





 



It will turn out looking like this!





 


Looking at the graph will help you figure out the domain, range, x-intercept, and y-intercept. However, from solving the inequality earlier, you have already figured out the domain.

Inequality: x ≥ 0
Domain: { x | x ≥ 0, XER }

Range: { y | y ≥ 0, YER}

X-intercept: 0
(Point that crosses x-axis)

Y-intercept: 0
(Point that crosses y-axis)