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 and its graphs 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 and its graphs https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:recognizing-functions/e/recog-func-2 2026-05-04T16:10:46.51963925Z Recognize functions from graphs Determine whether a given graph represents a function. Tomer Gal exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/linear-nonlinear-functions-tut/v/recognizing-linear-functions 2021-06-30T18:10:16Z Recognizing linear functions Learn to recognize if a function is linear. Sal Khan video https://cdn.kastatic.org/googleusercontent/8v73rsDx8EYHmfhyoxpuLHrfIQIPS_KP5QFDu0OXV8XQRftmbqwUeYfrALs8TATsDTve6T4kkmW1rbWe9xB0OyuC Recognizing linear functions Learn to recognize if a function is linear. https://cdn.kastatic.org/ka-youtube-converted/AZroE4fJqtQ.mp4/AZroE4fJqtQ.mp4 241 Functions and its graphs https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/linear-nonlinear-functions-tut/v/linear-and-nonlinear-functions-example-1 2021-06-30T18:10:09Z Linear & nonlinear functions: word problem Learn to determine if the relationship described in a word problem is a function. Sal Khan video https://cdn.kastatic.org/googleusercontent/kHZ18DRQyhI_DxfM596K4HQwtDUnFnEh2hu74A_-FzxiXhsYsVbKzfIMQ3GKNkP-6ezcF3XhvHx5c-lhEwLbL7lI6A Linear & nonlinear functions: word problem Learn to determine if the relationship described in a word problem is a function. https://cdn.kastatic.org/ka-youtube-converted/OWPVZoxNe-U.mp4/OWPVZoxNe-U.mp4 215 Functions and its graphs https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-linear-functions-modeling/v/interpreting-linear-graphs 2021-06-30T18:10:12Z Linear graphs word problems Sal discusses how we would go about making sense of the direction of a linear graph that represents a relationship between two real-world quantities. Sal Khan video https://cdn.kastatic.org/googleusercontent/H0hJcXLPMFBpYP3uQlIMxraf_R4iuewSEGTkUmjmZYDzD8JWbO5j9P1Ad9HGs97F_Z26MxZ4HhcEwZ17xu7i4Ghg Linear graphs word problems Sal discusses how we would go about making sense of the direction of a linear graph that represents a relationship between two real-world quantities. https://cdn.kastatic.org/ka-youtube-converted/xR9r38mZjK4.mp4/xR9r38mZjK4.mp4 305 Functions and its graphs https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/linear-nonlinear-functions-tut/e/linear-non-linear-functions 2024-01-22T04:00:33.388786774Z Linear & nonlinear functions Determine if a relationship is linear or nonlinear. Christopher Wobbles Seymour exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:applying-intercepts-and-slope/e/graphing-linear-functions-word-problems 2026-05-04T16:10:46.51963925Z Graphing linear relationships word problems Graph the line that represents a real-world relationship that is given verbally. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:absolute-value-piecewise-functions/x2f8bb11595b61c86:graphs-of-absolute-value-functions/v/graphing-absolute-value-functions 2022-11-16T04:22:43.7414897Z Graphing absolute value functions We can graph any absolute value equation of the form y=k|x-a|+h by thinking about function transformations (horizontal shifts, vertical shifts, reflections, and scalings). video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Graphing absolute value functions We can graph any absolute value equation of the form y=k|x-a|+h by thinking about function transformations (horizontal shifts, vertical shifts, reflections, and scalings). https://cdn.kastatic.org/ka-youtube-converted/v6Ct2OEmGNU.mp4/v6Ct2OEmGNU.mp4 371 Functions and its graphs https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:absolute-value-piecewise-functions/x2f8bb11595b61c86:graphs-of-absolute-value-functions/a/absolute-value-equations-and-graphs-review 2022-09-10T01:04:29.754011735Z Absolute value graphs review The general form of an absolute value function is f(x)=a|x-h|+k. From this form, we can draw graphs. This article reviews how to draw the graphs of absolute value functions. article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:absolute-value-piecewise-functions/x2f8bb11595b61c86:graphs-of-absolute-value-functions/e/graphs-of-absolute-value-functions 2026-04-07T23:36:17.218592739Z Graph absolute value functions Graph absolute value functions like f(x)=|x+3|+2. Tomer Gal exercise https://www.khanacademy.org/math/algebra-home/alg-radical-eq-func/alg-graphs-of-radical-functions/v/flipping-shifting-radical-functions 2020-11-06T18:53:40Z Transforming the square-root function Sal shows various examples of functions and their graphs that are a result of shifting and/or flipping y=√x. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZL4K0yGf-K6if6W2lc1CNnLb52liOP6-6lh_IuCxNLjvGGtWAJkkb5yyIBcEBcUM8aSU8WV3-dl1KxT92Ebs8whfmw Transforming the square-root function Sal shows various examples of functions and their graphs that are a result of shifting and/or flipping y=√x. https://cdn.kastatic.org/ka-youtube-converted/t5ry2rasWvI.mp4/t5ry2rasWvI.mp4 435 Functions and its graphs https://www.khanacademy.org/math/algebra-home/alg-radical-eq-func/alg-graphs-of-radical-functions/v/graphs-of-square-root-functions 2021-02-18T17:58:46Z Graphs of square-root functions Sal graphs y=√x. Then, he shows a few examples of how we can shift and stretch the graphs of y=√x and y=x^2, and how the equations of those graphs look. Sal Khan video https://cdn.kastatic.org/googleusercontent/gYhDetMHCwp0fuAQV9o_2UqUw1pycGUEG_MYizlIgNpDxxFPQgHPm36bh4YghniZBsqz2ZXncRrj0tF7Z1IWB_Lp Graphs of square-root functions Sal graphs y=√x. Then, he shows a few examples of how we can shift and stretch the graphs of y=√x and y=x^2, and how the equations of those graphs look. https://cdn.kastatic.org/ka-youtube-converted/outcfkh69U0.mp4/outcfkh69U0.mp4 901 Functions and its graphs https://www.khanacademy.org/math/algebra-home/alg-radical-eq-func/alg-graphs-of-radical-functions/v/radical-function-graphs-exercise 2020-11-06T18:53:42Z Square-root functions & their graphs Sal is given a drawing with four graphs and four formulas of square-root functions. He uses transformations to match each formula with its appropriate graph. Sal Khan video https://cdn.kastatic.org/googleusercontent/Njlqz5TGRRTXPXrEjvkJsAOUZ8kdQKIkTqhAPWSqkc0IwVfMfbcrfErBELg2AhL_bWYgOdzzYD5_7bOY8EhwkBOiBw Square-root functions & their graphs Sal is given a drawing with four graphs and four formulas of square-root functions. He uses transformations to match each formula with its appropriate graph. https://cdn.kastatic.org/ka-youtube-converted/Uteoh0PtWwI.mp4/Uteoh0PtWwI.mp4 222 Functions and its graphs https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:radical-graphs/v/graphing-square-and-cube-root 2022-10-06T23:23:50.639907812Z Graphing square and cube root functions We can graph various square root and cube root functions by thinking of them as transformations of the parent graphs y=√x and y=∛x. video https://cdn.kastatic.org/ka_thumbnails_cache/91757adc-05e6-472d-bf97-1e99d77ab7f2_1280_720_base.png Graphing square and cube root functions We can graph various square root and cube root functions by thinking of them as transformations of the parent graphs y=√x and y=∛x. https://cdn.kastatic.org/ka-youtube-converted/PI6IV7K3DbM.mp4/PI6IV7K3DbM.mp4 408 Functions and its graphs https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:radical-graphs/e/graphs-of-radical-functions 2024-12-05T04:14:54.285842675Z Graphs of square and cube root functions Given the formula of a square-root or a cube-root function, find the appropriate graph. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:radical-graphs/a/match-the-formula-of-a-radical-function-to-its-graph 2023-06-11T20:09:24.00592199Z Radical functions & their graphs Practice some problems before going into the exercise. article https://www.khanacademy.org/math/algebra-2-tx/xf7d2a662bc9ffb25:cubic-and-cube-root-functions-and-equations/xf7d2a662bc9ffb25:cubic-functions/v/transforming-a-cubic-function 2025-09-11T05:00:47.574338337Z Graphing cubic function transformations Sal demonstrates the relationship between changes to the equation of the parent function x^3 and transformations of its original graph. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/2b0854e2-6199-4015-bd1b-cda89ff22515_1280_720_base.png Graphing cubic function transformations Sal demonstrates the relationship between changes to the equation of the parent function x^3 and transformations of its original graph. https://cdn.kastatic.org/ka-youtube-converted/gpaRJMGFmyI.mp4/gpaRJMGFmyI.mp4 183 Functions and its graphs https://www.khanacademy.org/math/algebra-2-tx/xf7d2a662bc9ffb25:cubic-and-cube-root-functions-and-equations/xf7d2a662bc9ffb25:cubic-functions/e/graph-cubic-function-transformations 2025-07-01T01:15:48.63946125Z Graph cubic function transformations analyze the effect on the graph of 𝑓(𝑥) = 𝑥³ when 𝑓(𝑥) is replaced by 𝑎𝑓(𝑥), 𝑓(𝑏𝑥), 𝑓(𝑥 − 𝑐), and 𝑓(𝑥) + 𝑑 for specific positive and negative real values of 𝑎, 𝑏, 𝑐, and 𝑑 Nate Kinast exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/v/rewriting-a-quadratic-function-to-find-roots-and-vertex 2021-06-30T17:32:36Z Forms & features of quadratic functions Different forms of quadratic functions reveal different features of those functions. Here, Sal rewrites f(x)=x²-5x+6 in factored form to reveal its zeros and in vertex form to reveal its vertex. Sal Khan video https://cdn.kastatic.org/googleusercontent/IYWi7RoLLOMjWtLJvwRZz3CEG3Bma-p6nwFbm1bb8Ss8LqTcIrbzl4eyR9bkXrWuuliJKoYMAKpXggGwpvRUgVD- Forms & features of quadratic functions Different forms of quadratic functions reveal different features of those functions. Here, Sal rewrites f(x)=x²-5x+6 in factored form to reveal its zeros and in vertex form to reveal its vertex. https://cdn.kastatic.org/ka-youtube-converted/4Bc5-HRop5Y.mp4/4Bc5-HRop5Y.mp4 509 Functions and its graphs https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-linear-functions-modeling/v/application-problem-with-graph 2021-06-30T18:10:08Z Linear function example: spending money Sal solves an interesting application problem using a linear model. Sal Khan video https://cdn.kastatic.org/googleusercontent/N7JFfH1g-3yskAzS6tV48mRG4Z7rtWdlioieZ8pE5NTpX5JebiMh_pqh3JeA7J-rRYK8lWs0T19KL1DjOpUZq0li Linear function example: spending money Sal solves an interesting application problem using a linear model. https://cdn.kastatic.org/ka-youtube-converted/ljROszF_rqs.mp4/ljROszF_rqs.mp4 322 Functions and its graphs https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:applying-intercepts-and-slope/v/graphing-linear-functions-1 2021-06-30T18:10:07Z Linear functions word problem: fuel Sal is given a verbal description of a real-world relationship involving a truck's fuel consumption, and is asked to draw the graph that represents this relationship. video https://cdn.kastatic.org/googleusercontent/buUUegaAbCZNX9yqdcneiA7Ajctlol8D675Yp1szVRUq6MhLfq4rC2eXu8FV4nOK_gHFTYaGffsZlR3vY9F1qUk Linear functions word problem: fuel Sal is given a verbal description of a real-world relationship involving a truck's fuel consumption, and is asked to draw the graph that represents this relationship. https://cdn.kastatic.org/ka-youtube-converted/AAmVITyDXbc.mp4/AAmVITyDXbc.mp4 330 Functions and its graphs https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/constructing-linear-models-real-world/v/constructing-linear-functions-1 2021-06-30T18:10:05Z Linear functions word problem: iceberg Sal is given a verbal description of a real-world relationship involving a melting iceberg, and is asked to find the formula of the function that represents this relationship. video https://cdn.kastatic.org/googleusercontent/uAmo5jngH6EcOrO2ixoD0M2Oq9-Moa1JcA2hqPSDJXnFXRsqn_KBpzRWj3-ciWt0qMDNmzF4J7nS0R4-wrioprGT Linear functions word problem: iceberg Sal is given a verbal description of a real-world relationship involving a melting iceberg, and is asked to find the formula of the function that represents this relationship. https://cdn.kastatic.org/ka-youtube-converted/W7H-VcaSSu8.mp4/W7H-VcaSSu8.mp4 395 Functions and its graphs https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/constructing-linear-models-real-world/v/graphing-linear-functions-2 2021-06-30T18:10:16Z Linear functions word problem: pool Sal is given a verbal description of a real-world relationship involving a pool being filled with water, and is asked to draw the graph that represents this relationship. video https://cdn.kastatic.org/googleusercontent/apjfirlRniruVrF8RJ_CE4WP7ZuwJmWtbgznwa3qrVKCptn2LBiQMyvFW9A0W7Z7e7N5I5bJLQh5lweYoIKRj2mWYQ Linear functions word problem: pool Sal is given a verbal description of a real-world relationship involving a pool being filled with water, and is asked to draw the graph that represents this relationship. https://cdn.kastatic.org/ka-youtube-converted/zSVrr8K_CiI.mp4/zSVrr8K_CiI.mp4 192 Functions and its graphs 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