https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:evaluating-functions/v/what-is-a-function 2021-06-30T18:10:09Z What is a function? Functions assign a single output for each of their inputs. In this video, we see examples of various kinds of functions. Sal Khan video https://cdn.kastatic.org/googleusercontent/whRX1xQJEDdGcWfqUl8w5525C24vlDY-jZPlw-V9OTDxzG7Adv25nPLwbaP1FKUH4HK6R7YTRYoSCB9n4fLieb7A What is a function? Functions assign a single output for each of their inputs. In this video, we see examples of various kinds of functions. https://cdn.kastatic.org/ka-youtube-converted/kvGsIo1TmsM.mp4/kvGsIo1TmsM.mp4 477 Functions https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:functions/e/check-whether-the-relation-is-a-function 2026-04-07T22:23:57.656416987Z Check whether the relation is a function Test whether the given relation is a function or not exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/introduction-to-interval-notation 2021-03-29T04:28:53Z Intervals and interval notation Introducing intervals, which are bounded sets of numbers and are very useful when describing domain and range. We can use interval notation to show that a value falls between two endpoints. For example, -3≤x≤2, [-3,2], and {x∈ℝ|-3≤x≤2} all mean that x is between -3 and 2 and could be either endpoint.  video https://cdn.kastatic.org/googleusercontent/n02XI8jabgJMMuKAWpxBdCtHz0PVYHfxCLbfafHuBagTBkVk6nQsAoX1Ndy4notJe78NNnM9JmUT1LFEjFwnoPPe Intervals and interval notation Introducing intervals, which are bounded sets of numbers and are very useful when describing domain and range. We can use interval notation to show that a value falls between two endpoints. For example, -3≤x≤2, [-3,2], and {x∈ℝ|-3≤x≤2} all mean that x is between -3 and 2 and could be either endpoint.  https://cdn.kastatic.org/ka-youtube-converted/UJQkqV2zGv0.mp4/UJQkqV2zGv0.mp4 576 Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/domain-of-a-function-intro 2021-02-16T05:02:26Z What is the domain of a function? Functions assign outputs to inputs. The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited. video https://cdn.kastatic.org/googleusercontent/21E08TKEglE2LwI6L_u3pd3hzgeaBNUEuPWSxAINdNwYLqG68DD5gsX3HiOcqQTVk9Q36Q-a-pHPNJAeAIiAX7Ih What is the domain of a function? Functions assign outputs to inputs. The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited. https://cdn.kastatic.org/ka-youtube-converted/-DTMakGDZAw.mp4/-DTMakGDZAw.mp4 405 Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/range-of-a-function 2025-11-06T20:30:43.67988265Z What is the range of a function? The range of a function is the set of all possible outputs the function can produce. Some functions (like linear functions) can have a range of all real numbers, but lots of functions have a more limited set of possible outputs. video https://cdn.kastatic.org/googleusercontent/QtOI10gMX3xYAgVYOABaEWl-dNh_eWOQqQsX7MGvGh4PBTTXGsAZRjBbGSOk0IOesEL43E3nJ0OgSfBXRyWaCkT0 What is the range of a function? The range of a function is the set of all possible outputs the function can produce. Some functions (like linear functions) can have a range of all real numbers, but lots of functions have a more limited set of possible outputs. https://cdn.kastatic.org/ka-youtube-converted/96uHMcHWD2E.mp4/96uHMcHWD2E.mp4 399 Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/domain-and-range-from-graphs 2021-02-16T05:02:26Z Worked example: domain and range from graph Finding the domain and the range of a function that is given graphically. Sal Khan video https://cdn.kastatic.org/googleusercontent/N7YSTPtQJ08zW2VAcVIE-sImhLZ5Ju3p32DvOrnwwY_rm05BI_-9dgmWe7TZGIJpZ8UCpDQ7_Lf8SNo6Z6kkr_n0 Worked example: domain and range from graph Finding the domain and the range of a function that is given graphically. https://cdn.kastatic.org/ka-youtube-converted/sXP7VhU1gYE.mp4/sXP7VhU1gYE.mp4 214 Functions https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:functions/v/identity-and-constant-functions 2025-03-01T15:52:37.13987578Z Identity and constant functions This video looks at Identity and constant functions. We define them, draw them out, and find their domain and range. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Identity and constant functions This video looks at Identity and constant functions. We define them, draw them out, and find their domain and range. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. https://cdn.kastatic.org/ka-youtube-converted/uIUUY7X-0B0.mp4/uIUUY7X-0B0.mp4 357 Functions https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:functions/v/polynomial-function 2025-03-01T15:52:37.13987578Z Polynomial function What are polynomial functions? How do we draw them? What's their domain and range. Let's find that out in this video. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Polynomial function What are polynomial functions? How do we draw them? What's their domain and range. Let's find that out in this video. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. https://cdn.kastatic.org/ka-youtube-converted/clic1UxlHGQ.mp4/clic1UxlHGQ.mp4 457 Functions https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:functions/v/finding-domain-and-range-using-graph 2025-03-01T15:52:37.13987578Z Finding domain and range using graph Let's take a look at an example where plotting a graph can help us figure out the domain and range of a function. Even if that function is not a polynomial. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Since this function has a square root involved, we leverage algebra to figure out the domain. Range is calculated through visually observing the graph. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding domain and range using graph Let's take a look at an example where plotting a graph can help us figure out the domain and range of a function. Even if that function is not a polynomial. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Since this function has a square root involved, we leverage algebra to figure out the domain. Range is calculated through visually observing the graph. https://cdn.kastatic.org/ka-youtube-converted/A5kAC-L83lY.mp4/A5kAC-L83lY.mp4 234 Functions https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:functions/v/rational-functions 2025-03-01T15:52:37.13987578Z Rational functions What are rational functions? How do we plot them? What is their domain and range? Let's find out. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Rational functions What are rational functions? How do we plot them? What is their domain and range? Let's find out. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. https://cdn.kastatic.org/ka-youtube-converted/z2375vICoVI.mp4/z2375vICoVI.mp4 358 Functions https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:functions/v/modulus-function 2025-03-01T15:52:37.13987578Z Modulus function What is this mysterious modulus function? How do we define it? How do we plot it? What is its domain and range? Let's find out. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Modulus function What is this mysterious modulus function? How do we define it? How do we plot it? What is its domain and range? Let's find out. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. https://cdn.kastatic.org/ka-youtube-converted/CiZ1cUU1dgI.mp4/CiZ1cUU1dgI.mp4 227 Functions https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:functions/v/signum-function 2025-03-01T15:52:37.13987578Z Signum function What is this mysterious Signum function? How do we plot it? What is its domain and range? Let's find out. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Signum function What is this mysterious Signum function? How do we plot it? What is its domain and range? Let's find out. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. https://cdn.kastatic.org/ka-youtube-converted/7jrXMZpqewc.mp4/7jrXMZpqewc.mp4 181 Functions https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:relations-and-functions-ncert-new/x0419e5b3b578592a:functions/v/greatest-integer-function 2025-03-01T15:52:37.13987578Z Greatest Integer Function What is the Greatest Integer Function? How do we plot it? What is its domain and range? Let's find out. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Greatest Integer Function What is the Greatest Integer Function? How do we plot it? What is its domain and range? Let's find out. We break down the definition of the function given in set-builder form and plot the graph by connecting points on the cartesian plane. Domain and Range is calculated through visually observing the graph. https://cdn.kastatic.org/ka-youtube-converted/f0Ne5HIqnmI.mp4/f0Ne5HIqnmI.mp4 308 Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/e/domain_and_range_0.5 2026-04-08T22:00:50.923818222Z Domain and range from graph Given the graph of a function, determine its domain or range. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:recognizing-functions/v/graphical-relations-and-functions 2021-06-30T18:10:09Z Recognizing functions from graph Checking whether a given set of points can represent a function. For the set to represent a function, each domain element must have one corresponding range element at most. Sal Khan video https://cdn.kastatic.org/googleusercontent/Xx6kiGJjio_FaPEf-pejwFmHpp0eAvdClgbusZKQwmwE0oAI8EZv2SmDGHw1vHoBQtuwubAp11LwfP6m2tojnb9c Recognizing functions from graph Checking whether a given set of points can represent a function. For the set to represent a function, each domain element must have one corresponding range element at most. https://cdn.kastatic.org/ka-youtube-converted/qGmJ4F3b5W8.mp4/qGmJ4F3b5W8.mp4 247 Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:recognizing-functions/e/recog-func-2 2025-03-01T15:52:37.13987578Z Recognize functions from graphs Determine whether a given graph represents a function. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:evaluating-functions/e/evaluate-functions-from-their-graph 2025-03-01T15:52:37.13987578Z Evaluate functions from their graph Evaluate functions for specific inputs given the graph of the function.  Functions are written using function notation. Tomer Gal exercise