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 graph 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 graph 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 graph https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:evaluating-functions/v/understanding-function-notation-example-2 2021-06-30T18:10:10Z Worked example: Evaluating functions from graph Evaluating a function at x=-1 using the graph of that function. Sal Khan video https://cdn.kastatic.org/googleusercontent/rut742_LAfXpdb93Uk5lXue9m1yQuXStNvQkA3Ts6i_NZSMPTq2v6e4uPyFb9qkdLHy_pI1Jfzhg_aILSJVs9aYq Worked example: Evaluating functions from graph Evaluating a function at x=-1 using the graph of that function. https://cdn.kastatic.org/ka-youtube-converted/kzYtx_AqzjM.mp4/kzYtx_AqzjM.mp4 44 Functions and its graph 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 Functions and its graph 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 Functions and its graph 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 graph https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-function-intro/v/testing-if-a-relationship-is-a-function 2021-06-30T18:10:16Z Testing if a relationship is a function Learn to determine if points on a graph represent a function. Sal Khan video https://cdn.kastatic.org/googleusercontent/FluHhVFP9X1wEiiso95KbIKHQ7NIHPiW1GGAFg_ctgKl7ekOtSagOoZfWfF-UfCkuJR2YsafAWv8PxIygC91E8SL Testing if a relationship is a function Learn to determine if points on a graph represent a function. https://cdn.kastatic.org/ka-youtube-converted/3SO1BQQ9_1E.mp4/3SO1BQQ9_1E.mp4 143 Functions and its graph https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:recognizing-functions/v/recognizing-functions-example-2 2021-06-30T18:10:06Z Does a vertical line represent a function? Explaining why a vertical line doesn't represent a function. Sal Khan video https://cdn.kastatic.org/googleusercontent/KBKJG4cDX0COZ3lCEOrIDyGgTcHDUyTb2p8_vozx6S5qQHKVKCllv2pgKnINOvgyMBfpWswZnCh636d4ZZ56clDz Does a vertical line represent a function? Explaining why a vertical line doesn't represent a function. https://cdn.kastatic.org/ka-youtube-converted/_npwsLh0vws.mp4/_npwsLh0vws.mp4 100 Functions and its graph 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 https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/e/match-inputs-to-outputs-from-a-graph 2026-04-07T23:17:37.123726494Z Function inputs & outputs: graph Find all the inputs that correspond to a given function output, using the function's graph. Tomer Gal exercise 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