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https://www.intmath.com/functions-and-graphs/2a-domain-and-range.php

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Finding the domain and range from graphs

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Finding the domain and range from graphs

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The function f of x is graphed. What is its domain? So the way it's graphed right over here, we could assume that this is the entire function definition for f of x. So for example, if we say, well, what does f of x equal when x is equal to negative 9? Well, we go up here. We don't see it's graphed here. It's not defined for x equals negative 9 or x equals negative 8 and 1/2 or x equals negative 8. It's not defined for any of these values. It only starts getting defined at x equals negative 6. At x equals negative 6, f of x is equal to 5. And then it keeps getting defined. f of x is defined for x all the way from x equals negative 6 all the way to x equals 7. When x equals 7, f of x is equal to 5. You can take any x value between negative 6, including negative 6, and positive 7, including positive 7, and you just have to see-- you just have to move up above that number, wherever you are, to find out what the value of the function is at that point. So the domain of this function definition? Well, f of x is defined for any x that is greater than or equal to negative 6. Or we could say negative 6 is less than or equal to x, which is less than or equal to 7. If x satisfies this condition right over here, the function is defined. So that's its domain. So let's check our answer. Let's do a few more of these. The function f of x is graphed. What is its domain? Well, exact similar argument. This function is not defined for x is negative 9, negative 8, all the way down or all the way up I should say to negative 1. At negative 1, it starts getting defined. f of negative 1 is negative 5. So it's defined for negative 1 is less than or equal to x. And it's defined all the way up to x equals 7, including x equals 7. So this right over here, negative 1 is less than or equal to x is less than or equal to 7, the function is defined for any x that satisfies this double inequality right over here. Let's do a few more. The function f of x is graphed. What is its range? So now, we're not thinking about the x's for which this function is defined. We're thinking about the set of y values. Where do all of the y values fall into? Well, let's see. The lowest possible y value or the lowest possible value of f of x that we get here looks like it's 0. The function never goes below 0. So f of x-- so 0 is less than or equal to f of x. It does equal 0 right over here. f of negative 4 is 0. And then the highest y value or the highest value that f of x obtains in this function definition is 8. f of 7 is 8. It never gets above 8, but it does equal 8 right over here when x is equal to 7. So 0 is less than f of x, which is less than or equal to 8. So that's its range. Let's do a few more. This is kind of fun. The function f of x is graphed. What is its domain? So once again, this function is defined for negative 2. Negative 2 is less than or equal to x, which is less than or equal to 5. If you give me an x anywhere in between negative 2 and 5, I can look at this graph to see where the function is defined. f of negative 2 is negative 4. f of negative 1 is negative 3. So on and so forth, and I can even pick the values in between these integers. So negative 2 is less than or equal to x, which is less than or equal to 5.

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How to find domain and range from a graph (video) | Khan Academy

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The function f of x is graphed. What is its domain? So the way it's graphed right over here, we could assume that this is the entire function definition for f of x. So for example, if we say, well, what does f of x equal when x is equal to negative 9?

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Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.

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Finding the domain and range of a quadratic

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Finding the domain and range of a quadratic

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Sal finds the domain and the range of f(x)=3x^2+6x-2.

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This method uses factor theorem followed by algebraic long division

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How to factorise a cubic equation  (Method 1) : ExamSolutions

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Given a root, this method is for comparing coefficients

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Solving a cubic - part 3 - factorizing by comparing coefficients

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Subject: Math Level: high school, college Topic: factorizing a cubic equation by comparing coefficients; roots of a cubic NOTE: typo Coefficient on X squared should be "b-3a" not "b-3", which doesnt make a difference here as a=1. Sorry about that.

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This uses a multitude of methods to sketch a quadratic

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Sketching Quadratic Graphs : ExamSolutions

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Go to http://www.examsolutions.co.uk to see the full index, playlists and more videos on sketching quadratic graphs and other maths topics

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How to Graph a Piecewise Function with Three Inequalities : Fun With Math

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Subscribe Now: http://www.youtube.com/subscription_center?add_user=ehoweducation Watch More: http://www.youtube.com/ehoweducation Graphing a piecewise function with three inequalities will require you to first identify the different parts of the problem. Graph a piecewise function with three inequalities with help from a professional private tutor in this free video clip.

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This video is for C1 A level maths. It shows you how to solve a quadratic inequality by sketching graphs. It goes through a couple of examples and then has some practice questions to try.

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Introduction to Matrices

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Using second derivative to test for max/min.

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Using second derivative to test for max/min.

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"Extrema" means max/min

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How to use the SECOND DERIVATIVE TEST (KristaKingMath)

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► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course The second derivative test is a test you can use to find the extrema of a function. In order to use it, you'll need to be able to take the first and second derivatives of the function.

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Work your way through these

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Indices - Question and Worked Solution 3

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Indices Question 3 with Fully Worked Answer.

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How to differentiate.

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Go to http://www.examsolutions.net/maths-revision/index.php to see the main index of maths video tutorials

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Finding the equation of a tangent to a curve using the derivative. Watch to 5:55ish

This video is purely for tangent. If you need to find the eqn of the normal you will need to find the gradient of the tangent at that point, then find its negative reciprocal. This is then the gradient of the normal.

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❤︎² How to Find the Equation of a Tangent Line with Derivatives (mathbff)

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MIT grad shows how to find the equation of a tangent line using derivatives (Calculus). More videos with Nancy coming in 2017! To skip ahead: 1) For a BASIC example, skip to time 0:44. 2) For a more complex example that uses the CHAIN RULE, skip to time 5:58.

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Using the first derivative to find max/min "Extrema" means max/min!

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FIRST DERIVATIVE TEST to find the max and min (KristaKingMath)

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► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course The first derivative test is the tool you use to test the potential critical points of a function to see whether or not they are actually critical points. You can use the first derivative test to describe the behavior of the function on either side of the critical point.

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Transformations using matrices (Reflect and Rotate). Remember that you are doing a "Reflection OF something", therefore the transformation matrix must be written before the matrix containing coordinate information

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Transformations using matrices (Enlargement, stretch, sheer)

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Combining transformations. Remember that order matters. If you are doing a relfection, followed by a rotation, your matrices must read as follows:
rotation x reflection x coordinate

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Multiplying Matrices

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Multiplying Matrices - Example 1 - YouTube

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In this video I show how to multiply matrices! Need a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a4f-91da-90841e168246&TDC_OfferCode=e2bf363b-0cb8-4635-98c3-2b5211d0847a&subject=math&grade=undefined for a FREE 30 minute session! Multiplying Matrices - Two examples of multiplying a matrix by another matrix are shown.

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Using Sine/Cosine graphs to find values

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Using Tan graphs to find values

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Using special triangles and trig identities

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Using trig identities in proofs

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Proving a Trigonometric Indentity GCSE Further Maths revision Exam paper practice & help

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AQA Further Maths Level 2 (GCSE) June 2012 Paper 1 Question 16 Proving a Trigonometric Indentity GCSE Further Maths revision Exam paper practice & help The playlist for this exam paper is http://www.youtube.com/playlist?list=PL2De0DVeFj3VjXURPto5oCpbcwkAMBapP

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Geometry (Trigonometrical Identities) Ultimate revision guide for Further maths GCSE

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General revision

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BBC - Intermediate 2 Bitesize Mathematics - Trigonometry 2 : Revision, Page 8

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A BBC Bitesize secondary school revision resource for Intermediate 2 Mathematics

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This link goes with the revision videos and breaks down into topics

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Video Guides for AQA Level 2 Further Maths on Mr Barton Maths

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Below you will find Raw Maths' complete set of Further Maths videos, which I have organised into topic areas. The videos are simply excellent. Please Note: JerryJam on YouTube has a useful A* Guide to AQA Further Maths where he takes you through each chapter of the textbook.

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Geometry (Solving Trigonometrical Equations) Ultimate revision guide for Further maths GCSE