Graphs

Radical functions

A radical function is a function that contains a radical with a variable in its radicand.

These functions are radical functions:

f(x)=

g(x)=

Domain: The domain is all values that x can take on. The only problem you have with this function is that you cannot have a negative inside the square root. So you'll set the insides greater-than-or-equal-to zero, and solve.

Range: The range requires a graph.

Find the domain of f(x)=
The expression under the radical has to satisfy the condition 15-2x-x² > 0 for the function to take real values.

15-2x-x² > 0
(5+x)(3-x) > 0
Evaluating at several points:

Then the domain is [-5,3]

Determine the domain of the given function:

The domain is "all x"
The domain is "all x except the next point(s)"

The domain is given by the next intervals:

To use interval notation: Write -i to get the symbol and write i to get the symbol