How to Find Domain and Range of Radical Functions? (+FREE Worksheet!)
There are several different methods to identify the Domain and Range of Radical Functions. In this blog post, you will learn how to find the Domain and Range of Radical Functions.
Related Topics
- How to Add and Subtract Radical Expressions
- How to Multiply Radical Expressions
- How to Rationalize Radical Expressions
- How to Solve Radical Equations
- How to Simplify Radical Expressions
Rules for Finding Domain and Range of Radical Functions
- To find the domain of the function, find all possible values of the variable inside radical.
- Remember that having a negative number under the square root symbol is not possible. (For cubic roots, we can have negative numbers)
- To find the range, plugin the minimum and maximum values of the variable inside the radical.
Examples
Domain and Range of Radical Functions – Example 1:
Find the domain and range of the radical function. \(y=\sqrt{x-3}\)
Solution:
For domain: Find non-negative values for radicals: \(x-3≥0\)
Domain of functions: \(\sqrt{f(x)} →f(x)≥0\), Then solve \(x-3≥0→x-3+3 ≥0+3 → x≥3\)
Domain of the function \( y=\sqrt{x-3}: x≥3\)
For range: The range of a radical function of the form \(c\sqrt{ax+b}+k\) is:
\(f(x)≥k\)
For the function \(y=\sqrt{x-3}\), the value of \(k\) is \(0\). Then Range of the function \(y=\sqrt{x-3}: f(x)≥0\)
Domain and Range of Radical Functions – Example 2:
Find the domain and range of the radical function. \(y=\sqrt{x-8}+5\)
Solution:
For domain: Find non-negative values for radicals: \(x-8≥0\)
Domain of functions: \(\sqrt{f(x)} →f(x)≥0\), Then solve for \(x: x-8≥0→x-8+8 ≥ 0+8→ x≥8\)
Domain of the function \(y=\sqrt{x-8}+5:\) \(x≥8\)
For range: the range of a radical function of the form \(c\sqrt{ax+b}+k\) is \(f(x)≥k\)
For the function \(y=\sqrt{x-8}+5\), the value of \(k\) is \(5\). Then Range of the function \(y=\sqrt{x-8}+5 : f (x) ≥5\)
The Absolute Best Book for the Algebra I
Domain and Range of Radical Functions – Example 3:
Find the domain and range of the radical function. \(y=\sqrt{2x+4}+9\)
Solution:
For domain: Find non-negative values for radicals: \(2x+4≥0\)
Domain of functions: \(\sqrt{f(x)} →f(x)≥0\), Then solve for \(x: 2x+4≥0→x≥-2\)
Domain of the function \(y=\sqrt{2x+4}+9:\) \(x≥-2\)
For range: the range of a radical function of the form \(c\sqrt{ax+b}+k\) is \(f(x)≥k\)
For the function \(y=\sqrt{2x+4}+9\), the value of \(k\) is \(9\). Then Range of the function \(y=\sqrt{2x+4}+9 :\) \(f(x)≥9\)
Domain and Range of Radical Functions – Example 4:
Find the domain and range of the radical function. \(y=3\sqrt{2x-10}+6\)
Solution:
For domain: Find non-negative values for radicals: \(2x-10≥0\)
Domain of functions: \(\sqrt{f(x)} →f(x)≥0\), Then solve for \(x: 2x-10≥0→x≥5\)
Domain of the function \(y=3\sqrt{2x-10}+6:\) \(x≥5\)
For range: the range of a radical function of the form \(c\sqrt{ax+b}+k\) is \(f(x)≥k\)
For the function \(y=3\sqrt{2x-10}+6\), the value of \(k\) is \(6\). Then Range of the function \(y=3\sqrt{2x-10}+6:\) \(f(x)≥6\)
Exercises for Domain and Range Radical Functions
Identify the Domain and Range
- \(\color{blue}{y=\sqrt{x-1}}\)
- \(\color{blue}{y=2\sqrt{x+3}}\)
- \(\color{blue}{y=\sqrt{x-5}}\)
- \(\color{blue}{y=\sqrt{x+4}+2}\)
Sketch the graph of the function
5. \(\color{blue}{y=\sqrt{x}-2}\)
6. \(\color{blue}{y=3\sqrt{x}-1}\)
- \(\color{blue}{x≥1,f(x)≥0}\)
- \(\color{blue}{x≥-3,f(x)≥0}\)
- \(\color{blue}{x≥5,f(x)≥0}\)
- \(\color{blue}{x≥-4,f(x)≥2}\)
5. \(\color{blue}{y=\sqrt{x}-2}\)
6. \(\color{blue}{y=3\sqrt{x}-1}\)
The Absolute Best Book for the Algebra Test
Related to This Article
More math articles
- The Ultimate Algebra 2 Course
- The Best PERT Math Worksheets: FREE & Printable
- Algebra Puzzle – Challenge 55
- How to Prepare for the PSAT 8/9 Math Test?
- The Ultimate 7th Grade PEAKS Math Course (+FREE Worksheets)
- How to Write Linear Functions Word Problems
- 10 Most Common 4th Grade Georgia Milestones Assessment System Math Questions
- 5th Grade IAR Math Worksheets: FREE & Printable
- Full-Length 8th Grade SBAC Math Practice Test-Answers and Explanations
- How to Find the Equation of a Regression Line and Interpret Regression Lines
What people say about "How to Find Domain and Range of Radical Functions? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.