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
- How to Find Modulus (Absolute Value) and Argument (Angle) of Complex Numbers?
- FREE 6th Grade ACT Aspire Math Practice Test
- Top 10 6th Grade MEAP Math Practice Questions
- How Is the ACCUPLACER Test Scored?
- 4th Grade Common Core Math Worksheets: FREE & Printable
- ACCUPLACER Math Practice Test Questions
- 5 Best SAT Mаth Books fоr Studеntѕ Prераring fоr thе SAT Tеѕt
- How to Define Limits Analytically Using Correct Notation?
- Top 10 Tips You MUST Know to Retake the HiSET Math
- How to Convert, Compare, Add, and Subtract Mixed Customary Units?
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.