Name:_____________________________
Date:________________________
Domain of Radical Functions
Domain - The set of values of the independent variable(s) for which a function or relation is
defined.
There are two reasons why x would be undefined.
1. You can’t take the square root of a negative number.
2. You can’t divide by zero.
Steps
1. Determine the index of the radical.
2. If the index is an even number, set the expression inside the radical greater than or equal to
zero.
If the index is an odd number, the domain is all real numbers.
3. Solve the equation found in step 2.
4. Write the answer using interval notation.
Interval notation - A method of writing down a set of numbers. Usually, this is used to describe
a certain span or group of spans of numbers along an axis, such as an x-axis.
Example 1 - Find the domain of the function, and describe the domain using interval notation.
𝑓(𝑥) = √5 − 8𝑥
Example 2 - Find the domain of the function, and describe the domain using interval notation.
𝑓(𝑥) = √𝑥 + 4
Example 3 - Find the domain of the function, and describe the domain using interval notation.
𝑓(𝑥) = √𝑥 + 4
Name:_____________________________
Date:________________________
Example 4 - Find the domain of the function, and describe the domain using interval notation.
3
𝑓(𝑥) = √𝑥 + 1 – 4
Example 5 - Find the domain of the function, and describe the domain using interval notation.
4
𝑓(𝑥) = √2𝑥 + 9
Example 6 - Find the domain of the function, and describe the domain using interval notation.
5
𝑓(𝑥) = √11 − 7𝑥
Example 7 - Find the domain of the function, and describe the domain using interval notation.
4
𝑓 (𝑥) = √2𝑥 2 − 18
Example 8 - Find the domain of the function, and describe the domain using interval notation.
𝑓(𝑥) =
𝑥+3
√𝑥−8
Example 9 - Find the domain of the function, and describe the domain using interval notation.
𝑓(𝑧) = √𝑧 2 + 2𝑧 − 8