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/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/a/functions-faq 2023-01-05T23:21:50.258247214Z Functions: FAQ Frequently asked questions about functions article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:evaluating-functions/e/functions_1 2026-03-24T23:41:07.080866137Z Evaluate functions Evaluate functions for specific inputs given the formula of the function.  Functions are written using function notation. Tomer Gal exercise 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/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:determining-the-domain-of-a-function/v/determine-values-domain 2022-09-10T01:04:29.754011735Z Determining whether values are in domain of function Sal shows how to test whether or not a value is or isn't in the domain of a function. video https://cdn.kastatic.org/googleusercontent/v4m-Zyja9R7wKI3PpddsyYyFTFsOEXq-mIxvYHX1940MPxl-nS8UxzktxYAedO-gXBj2FutiCvJ0fBctHni_CUelgA Determining whether values are in domain of function Sal shows how to test whether or not a value is or isn't in the domain of a function. https://cdn.kastatic.org/ka-youtube-converted/LdbrNNheFg8.mp4/LdbrNNheFg8.mp4 297 Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:determining-the-domain-of-a-function/e/values-in-domain 2026-04-07T23:55:07.30621384Z Identifying values in the domain Practice identifying values that are and are not in the domain of a function. Jeff Dodds exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/v/introduction-to-function-inverses 2021-06-30T17:32:40Z Intro to inverse functions Sal explains what inverse functions are. Then he explains how to algebraically find the inverse of a function and looks at the graphical relationship between inverse functions. Sal Khan video https://cdn.kastatic.org/googleusercontent/ftP3WqomYgOSNNJDBNLb8gpsbRrlkSkKS4SlMRckoGmmIRud0-yHWYXE6DNpwZKfq_CDk2f3qKYYTyvRN1Zllq8 Intro to inverse functions Sal explains what inverse functions are. Then he explains how to algebraically find the inverse of a function and looks at the graphical relationship between inverse functions. https://cdn.kastatic.org/ka-youtube-converted/W84lObmOp8M.mp4/W84lObmOp8M.mp4 545 Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/a/intro-to-inverse-functions 2026-03-26T05:20:35.16058035Z Intro to inverse functions Learn what the inverse of a function is, and how to evaluate inverses of functions that are given in tables or graphs. article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/v/understanding-function-inverses-example 2021-06-30T17:32:34Z Graphing the inverse of a linear function Sal is given a line segment on the coordinate plane, and he graphs the inverse of the function represented by that segment. video https://cdn.kastatic.org/googleusercontent/a8NqOc1YiY0yqwVIcW9h9xR6fvL_t0tmMBpRR3w8fHs0hYodTcqEWkESo-exP5BTBHqXfy1TD1Ko_NZTK-_B2MHQ Graphing the inverse of a linear function Sal is given a line segment on the coordinate plane, and he graphs the inverse of the function represented by that segment. https://cdn.kastatic.org/ka-youtube-converted/KPeS2gdizhQ.mp4/KPeS2gdizhQ.mp4 137 Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/e/understanding-inverse-functions 2026-04-07T23:36:17.218592739Z Evaluate inverse functions Practice evaluating the inverse function of a function that is given either as a formula, or as a graph, or as a table of values. Stacy Beaudoin exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/v/function-inverse-example-1 2021-06-30T17:32:37Z Finding inverse functions: linear Sal finds the inverses of f(x)=-x+4 and g(x)=-2x-1. Sal Khan video https://cdn.kastatic.org/googleusercontent/1a08_e0zk7y2t7AGJ-bPOX_XxYYuROBbx6j6aUM8BaGQf3_YHATZDoOhCoLO2GyS0ZPApfU1vBaXsvgzV6OMxAGO Finding inverse functions: linear Sal finds the inverses of f(x)=-x+4 and g(x)=-2x-1. https://cdn.kastatic.org/ka-youtube-converted/wSiamij_i_k.mp4/wSiamij_i_k.mp4 404 Functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/e/algebraically-finding-inverses 2026-03-10T04:30:37.966653692Z Find inverses of linear functions Practice finding the formula of the inverse function of a given linear function. Stacy Beaudoin exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/function-composition 2023-04-03T21:40:12.365083232Z Intro to composing functions This video is about composing functions, which is the process of building up a function by composing it from other functions. It explains how to evaluate the composition of functions step by step, using examples with three different function definitions: f (x), g(t), and h(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/oFlXj7HzyrhyxvG_Yu6VUREb1D8SFPYfTXdYMjNZ8IRCsqcb7iQ6JMTPIaErn9TpUBuxsSjuXVfmv2B0l23ffSgYbQ Intro to composing functions This video is about composing functions, which is the process of building up a function by composing it from other functions. It explains how to evaluate the composition of functions step by step, using examples with three different function definitions: f (x), g(t), and h(x). https://cdn.kastatic.org/ka-youtube-converted/wUNWjd4bMmw.mp4/wUNWjd4bMmw.mp4 375 Functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/a/introduction-to-function-composition 2024-02-16T22:17:57.248778253Z Intro to composing functions Learn why we'd want to compose two functions together by looking at a farming example. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/evaluating-composite-functions 2022-10-07T00:22:18.752150461Z Evaluating composite functions Sal evaluates (h⚬g)(-6) for g(x)=x²+5x-3 and h(y)=3(y-1)²-5. video https://cdn.kastatic.org/ka_thumbnails_cache/e6f1b3f6-3917-42a6-8cc0-695655b73fd6_1280_720_base.png Evaluating composite functions Sal evaluates (h⚬g)(-6) for g(x)=x²+5x-3 and h(y)=3(y-1)²-5. https://cdn.kastatic.org/ka-youtube-converted/lxtlwnCV-HM.mp4/lxtlwnCV-HM.mp4 250 Functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/e/evaluate-composite-functions-from-formulas 2025-03-03T19:47:54.930712342Z Evaluate composite functions Given the formulas of two functions, evaluate the composition of the two functions at a given input. Stacy Beaudoin exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/evaluating-composite-functions-using-tables 2021-05-05T14:53:16Z Evaluating composite functions: using tables Given tables of values of the functions f and g, Sal evaluates f(g(0)) and g(f(0)). video https://cdn.kastatic.org/googleusercontent/01vR766yhJWW4lupJHY2EZKEx5u0ey3JdSmnxYQJptdca9tIHrGXqZeV5jMUkb4lG1w1EfVdvSP_GdVDKu0pG1lx_A Evaluating composite functions: using tables Given tables of values of the functions f and g, Sal evaluates f(g(0)) and g(f(0)). https://cdn.kastatic.org/ka-youtube-converted/FR8JH6IldsE.mp4/FR8JH6IldsE.mp4 250 Functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/evaluating-composite-functions-using-graphs 2022-10-07T00:22:18.752150461Z Evaluating composite functions: using graphs Given the graphs of the functions f and g, Sal evaluates g(f(-5)). video https://cdn.kastatic.org/ka_thumbnails_cache/2702228b-0418-4025-8a41-fa9fbe01fb58_1280_720_base.png Evaluating composite functions: using graphs Given the graphs of the functions f and g, Sal evaluates g(f(-5)). https://cdn.kastatic.org/ka-youtube-converted/oORnGaJp1pk.mp4/oORnGaJp1pk.mp4 182 Functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/e/evaluate-composite-functions-from-graphs-and-tables 2026-03-08T08:10:35.408394002Z Evaluate composite functions: graphs & tables Given the graphs or tables of values of two functions, evaluate the composition of those functions for a given input. Charlotte Auen exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/new-function-from-composition 2023-07-18T22:48:45.033562364Z Finding composite functions Through a worked example involving f(x)=√(x²-1) and g(x)=x/(1+x), learn about function composition: the process of combining two functions to create a new function. This involves replacing the input of one function with the output of another function. Also note that the composition of two functions is typically not the same as their composition in the reverse order. Sal Khan video https://cdn.kastatic.org/googleusercontent/5uNkRakTQjdWVltWmPnETUCEp1SkdEtER8bW9NjVyBzMQ31W2yM4ZMutYYnxEEsIpytv1kXUxXoCMz4zCeF7CeI1UA Finding composite functions Through a worked example involving f(x)=√(x²-1) and g(x)=x/(1+x), learn about function composition: the process of combining two functions to create a new function. This involves replacing the input of one function with the output of another function. Also note that the composition of two functions is typically not the same as their composition in the reverse order. https://cdn.kastatic.org/ka-youtube-converted/_b-2rZpX5z4.mp4/_b-2rZpX5z4.mp4 177 Functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/e/compose-functions 2025-05-05T08:14:25.350149109Z Find composite functions Given the formulas of two functions, find the formula of their composition. Charlotte Auen exercise