Laura received her Master's degree in Pure Mathematics from Michigan State University, and her Bachelor's degree in Mathematics from Grand Valley State University. She has 20 years of experience teaching collegiate mathematics at various institutions.
How to Graph y=sqrt(x)
Steps to Solve
In order to graph y = sqrt(x), we first want to get a better idea of how the graph is going to look. We can do this by making some simple observations. The first thing we should take notice of is the domain and range of y = sqrt(x).
The domain consists of all the inputs, or numbers, we plug in for x that make sqrt(x) defined. Since we can't take the square root of negative numbers without getting a non-real number out, and we can't graph non-real numbers on the coordinate axis, the domain of y = sqrt(x) is all real numbers greater than or equal to 0.
The range consists of all of the outputs, or the values y takes on. Based on the fact that our domain consists of all real numbers greater than or equal to 0, the numbers we will get back out will be real numbers greater than or equal to 0. This leads to the following two facts regarding the domain and range of y = sqrt(x):
- The domain of y=sqrt(x) is all real numbers greater than or equal to 0.
- The range of y=sqrt(x) is all real numbers greater than or equal to 0.
This information gives us an idea of where our graph will be on the coordinate axis as is illustrated in this image:
Now let's plug in some strategic numbers for x and find the corresponding y values. This will give us an idea of the shape of the graph.
x | y |
---|---|
0 | 0 |
1 | 1 |
4 | 2 |
9 | 3 |
16 | 4 |
25 | 5 |
Our chart displays different points that will be on the graph. We can tell that the graph will be rising from left to right since y increases as x increases. We also see that the graph starts off rising fairly quickly, but then rises more and more slowly since the y values go up by 1 as the x values get more and more spaced out.
We now have a general idea of how the graph is behaving. The next thing we need to do is plot some of the points in our chart on a graph.
We see the points take on the pattern we expected. The graph will rise from left to right, and it starts off rising quickly, but then slows down. The last thing we need to do is to connect the dots in a smooth line.
We've found the following graph to be the graph of y = sqrt(x).
An error occurred trying to load this video.
Try refreshing the page, or contact customer support.
You must cCreate an account to continue watching
Register to view this lesson
As a member, you'll also get unlimited access to over 84,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.
Get unlimited access to over 84,000 lessons.
Try it nowAlready registered? Log in here for access
BackYou're on a roll. Keep up the good work!
Just checking in. Are you still watching?
Yes! Keep playing.Graphing Alternative
There is another way to go about graphing y = sqrt(x), and it revolves around the fact that if we take the function y = x2 and restrict its domain to all real numbers greater than or equal to 0, then we have the inverse function of y = sqrt(x).
Inverse functions are functions that basically undo each other. That is, if we take an input a and plug it into a function f, then we get an output of b. If we plug that output b into the inverse function of f, then we get a back out. This gives way to the following property of inverse functions:
If (a,b) is on the graph of the function f, then (b,a) is on the graph of the inverse function of f.
This is a lot of information, and you are probably wondering how this will help us to graph y = sqrt(x). Well, as it turns out, the graphs of inverse functions are mirror images of one another over the line y = x. We can use this to help us derive the graph of y = sqrt(x) from the graph of y = x2, where x is greater than or equal to 0.
We start with the graph of y = x2 with the restricted domain.
Next, we draw the line y = x and reflect the graph over that line. For accuracy, we can use our fact to take points on y = x2 and interchange the coordinates to find points on y = sqrt(x).
We can see that graph y = sqrt(x) using its inverse function y = x2 with x greater than or equal to 0. Pretty handy, huh?
Lesson Summary
The square root function of y = sqrt(x) is a function that shows up often in many different areas, so it is useful to have an idea of what the graph of this function looks like. The great thing is, if we forget what it looks like, we now have a couple of ways to go about graphing it, including using the inverse function.
To unlock this lesson you must be a Study.com Member.
Create your account
Register to view this lesson
Unlock Your Education
See for yourself why 30 million people use Study.com
Become a Study.com member and start learning now.
Become a MemberAlready a member? Log In
BackHow to Graph y=sqrt(x)
Related Study Materials
- Math Courses
- Algebra Courses
- Study Courses
- Homework Help Courses
- High School Courses
- High School Geometry: Homework Help Resource
- High School Geometry: Help and Review
- High School Geometry: Tutoring Solution
- CLEP College Algebra: Study Guide & Test Prep
- College Mathematics: Certificate Program
- Introduction to Statistics: Certificate Program
- Precalculus: Certificate Program
- High School Precalculus: Homework Help Resource
- High School Algebra II: Homework Help Resource
- Precalculus Algebra: Certificate Program
- College Algebra: Certificate Program
- Holt McDougal Algebra 2: Online Textbook Help
- SAT Subject Test Mathematics Level 1: Tutoring Solution
Browse by Courses
- How to Write Numbers in Words: Rules & Examples
- How to Divide Fractions: Whole & Mixed Numbers
- How to Solve Two-Step Equations with Fractions
- How to Do Cross Multiplication of Fractions
- How to Write 0.0005 in Scientific Notation: Steps & Tutorial
- Quiz & Worksheet - Roman Numerals from 1 to 20
- Quiz & Worksheet - Simplifying a Multiplication Expression
- Quiz & Worksheet - Adding Positive & Negative Integers
- Quiz & Worksheet - Adding & Subtracting Negative Numbers
- Quiz & Worksheet - Integer Inequalities with Absolute Values
- NY Regents - Introduction to Geometric Figures: Tutoring Solution
- NY Regents - Similar Polygons: Tutoring Solution
- NY Regents - Quadrilaterals: Tutoring Solution
- NY Regents - Circular Arcs and Circles: Tutoring Solution
- NY Regents - Analytical Geometry: Tutoring Solution
Browse by Lessons
- Biology 202L: Anatomy & Physiology II with Lab
- Biology 201L: Anatomy & Physiology I with Lab
- California Sexual Harassment Refresher Course: Supervisors
- California Sexual Harassment Refresher Course: Employees
- Sociology 110: Cultural Studies & Diversity in the U.S.
- Sequences and Series in Math
- Application and Optimization of Derivatives
- Derivative Theorems, Rules and Graphs
- Basic Measures in Statistics
- Mathematical Probabilities
- Addressing Cultural Diversity in Distance Learning
- New Hampshire Homeschooling Laws
- Setting Student Expectations for Distance Learning
- COVID-19 Education Trends that are Here to Stay
- What to Do with a COVID-19 College Gap Year
- Active Learning Strategies for the Online Classroom
- How to Promote Online Safety for Students in Online Learning
Latest Courses
- Irony in A Raisin in the Sun
- Observing Changes in Natural Phenomena Over Time
- Rene Descartes' Math Contributions Lesson for Kids: Biography & Facts
- Allan Schnaiberg: The Treadmill of Production & Environmental Sociology
- The Food Web of the Mojave Desert
- The Boreal Forest Food Web
- Uchendu in Things Fall Apart
- Quiz & Worksheet - Anna of Byzantium Book Summary
- Quiz & Worksheet - Songhai Trade & Government
- Quiz & Worksheet - Japanese Carp Kites
- Quiz & Worksheet - Long Way Down Theme & Genre
- Flashcards - Real Estate Marketing Basics
- Flashcards - Promotional Marketing in Real Estate
- Science Worksheets | Printable Science Worksheets for Teachers
- 10th Grade Math Worksheets & Printables
Latest Lessons
- Abnormal Psychology: Certificate Program
- AP US History: Homework Help Resource
- 11th Grade English Textbook
- Linear Algebra: Help & Tutorials
- Understanding the Effects of Globalization in Business
- Reproductive Sequence for the MCAT: Help and Review
- Reading and Understanding Essays in 11th Grade
- Quiz & Worksheet - Characteristics of True Experimental Design
- Quiz & Worksheet - Gilligan's Theory of Moral Development
- Quiz & Worksheet - Cognitive Perspective of Learning & Information Processing
- Quiz & Worksheet - Ionic Compound Formation & Properties
- Quiz & Worksheet - Octet Rule with the Lewis Structures of Atoms
Popular Courses
- Gross Domestic Product: Items Excluded from National Production
- Geometry Assignment - Using Triangles, Quadrilaterals, Other Polygons & Circles
- How to Earn a Digital Badge
- Columbus Day Activities for Kids
- Reading Games for Kids
- Fractions Games for Kids
- How to Pass the Physics Regents Exam
- Imperialism Lesson Plan
- 3rd Grade Math Centers
- Michigan's Grade Level Content Expectations (GLCEs)
- Math Poster Ideas
- How to Pass the California Bar Exam
Popular Lessons
Math
Social Sciences
Science
Business
Humanities
Education
History
Art and Design
Tech and Engineering
- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers
Health and Medicine
- Use the given graph of f(x)=\sqrt x to find a number \delta such that if |x-4| < \delta then |\sqrt x-2|<0.4.
- Give the domain of the square root of (x - 3).
- Find the domain and range of the function. (Enter your answers using interval notation.) h(x) = square root {4 - x^2} Sketch the graph of the function.
- Find the domain of the function y = \sqrt{25 x^2} . Then graph the function.
- Graph f(x) = \sqrt{x}. What is its domain?
- Sketch the graph of the function by first making a table of values. f(x) =\sqrt{x+4}
Explore our library of over 84,000 lessons
- Create a Goal
- Create custom courses
- Get your questions answered