https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-function-intro/v/relations-and-functions 2021-06-30T18:10:09Z Relations and functions Learn to determine if a relation given by a set of ordered pairs is a function. Sal Khan video https://cdn.kastatic.org/googleusercontent/_QXa2dqNYNQ75UOKQ9lalz11LItO7kWgj6mKmI5-Y6VuzzRQgItN43D_HVLYTNTL7D_icdCyMGdWyFRqI61ftbeF Relations and functions Learn to determine if a relation given by a set of ordered pairs is a function. https://cdn.kastatic.org/ka-youtube-converted/Uz0MtFlLD-k.mp4/Uz0MtFlLD-k.mp4 417 Relations and Functions 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 Relations and Functions 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 Relations and 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 Relations and 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 Relations and 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 Relations and Functions 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 Relations and Functions https://www.khanacademy.org/math/algebra-home/alg-functions/alg-combining-functions/v/sum-of-functions 2021-06-30T17:32:36Z Adding functions Given that f(x)=9-x^2 and g(x)=5x^2+2x+1, Sal finds (f+g)(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/vQo4H2MOShkJUwO2-h3Bj6ZvskipyaGS2sDl8f9RQSlUzaUiSg1HAaJGpn2r5qK_MFGruIxMkek26UyuWUfDQJXXDQ Adding functions Given that f(x)=9-x^2 and g(x)=5x^2+2x+1, Sal finds (f+g)(x). https://cdn.kastatic.org/ka-youtube-converted/n34dqyVCXs4.mp4/n34dqyVCXs4.mp4 153 Relations and Functions https://www.khanacademy.org/math/algebra-home/alg-functions/alg-combining-functions/v/difference-of-functions 2021-06-30T17:32:38Z Subtracting functions Given that f(x)=2x√5-4 and g(x)=x^2+2x√5-1, Sal finds (g-f)(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/xl5HyNwZdnhKN5mhN2CIDDn3bMEV0T0scv9BRIbN5KBHYDmda4ERpzjR4OitpkO96VWeTcymCUeXgjT5RZ8XV2XG Subtracting functions Given that f(x)=2x√5-4 and g(x)=x^2+2x√5-1, Sal finds (g-f)(x). https://cdn.kastatic.org/ka-youtube-converted/6arI8XhLZ9o.mp4/6arI8XhLZ9o.mp4 136 Relations and Functions https://www.khanacademy.org/math/algebra-home/alg-functions/alg-combining-functions/v/product-of-functions 2021-06-30T17:32:39Z Multiplying functions Sal solves the following problem: given that f(x)=7x-5 and g(x)=x^3+4x, find (f*g)(x). He explains that generally, (f*g)(x)=f(x)*g(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/xKaLOaIfWxXnd1Z2TGBedcxXMuYJlrjbh1O9Dq_DS0VwjrP6X0C8UfVOk-4EUlaP0bQlKB5cRsP4QgPNUCKDNhP7 Multiplying functions Sal solves the following problem: given that f(x)=7x-5 and g(x)=x^3+4x, find (f*g)(x). He explains that generally, (f*g)(x)=f(x)*g(x). https://cdn.kastatic.org/ka-youtube-converted/JKvmAexeMgY.mp4/JKvmAexeMgY.mp4 180 Relations and Functions https://www.khanacademy.org/math/algebra-home/alg-functions/alg-combining-functions/v/quotient-of-functions 2021-06-30T17:32:38Z Dividing functions Sal solves the following problem: given that f(x)=2x^2+15x-8 and g(x)=x^2+10x+16, find (f/g)(x). He explains that generally, (f/g)(x)=f(x)/g(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/LQhm8DE94i6gbuh6j4QkFQqISyUHwm__xaq5lZrD0uKKZ5HkryZQkfbRJHqZlHLF4gBgiupsp3c-1Dye81jxnt9- Dividing functions Sal solves the following problem: given that f(x)=2x^2+15x-8 and g(x)=x^2+10x+16, find (f/g)(x). He explains that generally, (f/g)(x)=f(x)/g(x). https://cdn.kastatic.org/ka-youtube-converted/u9v_bakOIcU.mp4/u9v_bakOIcU.mp4 378 Relations and Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/v/matching-function-input-to-output-with-graph 2021-05-05T14:53:16Z Worked example: matching an input to a function's output (graph) Sal finds the input value for which g(x)=-2 given the graph of g. video https://cdn.kastatic.org/googleusercontent/a8rSDx-YrrM8R6maqN-siR6uwCmMF1ycoEnZyTl5EdC4C6P79C1R4-lVsb_86V-c8R-1Kax9Kl2MlE6IK-cNMa6X Worked example: matching an input to a function's output (graph) Sal finds the input value for which g(x)=-2 given the graph of g. https://cdn.kastatic.org/ka-youtube-converted/0Rmmynff5Yc.mp4/0Rmmynff5Yc.mp4 67 Relations and Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/v/different-inputs-giving-same-value-for-function 2021-05-05T14:53:18Z Worked example: two inputs with the same output (graph) Sal finds the input value other than -5 for which f(x)=f(-5), given the graph of f. video https://cdn.kastatic.org/googleusercontent/T9LS6JQUy_PBE6C53by--XCd1rUoo_Pz9PjxNKZ_e6ajw46YGN7ddiigWDIbk_cgr6OWA50xSkyGDr18pMQ_6BIZ Worked example: two inputs with the same output (graph) Sal finds the input value other than -5 for which f(x)=f(-5), given the graph of f. https://cdn.kastatic.org/ka-youtube-converted/qSktOkaW6EA.mp4/qSktOkaW6EA.mp4 108 Relations and Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/v/finding-input-given-function-output-formula 2021-04-30T08:40:48Z Worked example: matching an input to a function's output (equation) Sal finds the input value for which f(t)=13, given that f(t)=-2t+5. video https://cdn.kastatic.org/googleusercontent/JlJoN6LFEZi-W_mdBLaiL4xij78NQhAsoFU5tLK680GG1i2oZEAiTv7j18Zivy8xlegoVTkMm5Y5Cz_CzxEyQl_N Worked example: matching an input to a function's output (equation) Sal finds the input value for which f(t)=13, given that f(t)=-2t+5. https://cdn.kastatic.org/ka-youtube-converted/tJBQZ3PUkPo.mp4/tJBQZ3PUkPo.mp4 100 Relations and Functions https://www.khanacademy.org/math/ka-revision-class-11-math/x64e5efbb29d87707:week-1-revision-ncert-class-11-math/x64e5efbb29d87707:relations-and-functions-revision-ncert-class-11-math/e/revision-relations-and-functions-ncert-class-11-math 2026-04-08T01:19:59.083532605Z Revision Relations and Functions Practice Problems for revision of Relations and Functions. Satya Swaroop exercise