https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:scale/v/scaling-functions-intro 2022-10-06T23:23:50.639907812Z Scaling functions introduction The graph y=k⋅f(x) (where k is a real number) is similar to the graph y=f(x), but each point's distance from the x-axis is multiplied by k. A similar thing happens when we graph y=f(k⋅x), only now the distance from the y-axis changes. These operations are called "scaling." video https://cdn.kastatic.org/ka_thumbnails_cache/9e55d08c-6d8f-422b-835d-9a14d1923950_1280_720_base.png Scaling functions introduction The graph y=k⋅f(x) (where k is a real number) is similar to the graph y=f(x), but each point's distance from the x-axis is multiplied by k. A similar thing happens when we graph y=f(k⋅x), only now the distance from the y-axis changes. These operations are called "scaling." https://cdn.kastatic.org/ka-youtube-converted/1lt6a77OmLU.mp4/1lt6a77OmLU.mp4 363 Scaling functions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:scale/v/vert-function-scaling 2023-07-14T23:21:51.065682509Z Scaling functions vertically: examples The function k⋅f(x) is a vertical scaling of f. See multiple examples of how we relate the two functions and their graphs, and determine the value of k. video https://cdn.kastatic.org/ka_thumbnails_cache/43ae16dc-37ac-4a89-9f00-138f3c7e0cdf_1280_720_base.png Scaling functions vertically: examples The function k⋅f(x) is a vertical scaling of f. See multiple examples of how we relate the two functions and their graphs, and determine the value of k. https://cdn.kastatic.org/ka-youtube-converted/tRCEBtKLqEw.mp4/tRCEBtKLqEw.mp4 309 Scaling functions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:scale/e/scale-functions-vertically 2023-07-10T01:26:19.256593834Z Scale functions vertically If we multiply a function by a constant, we scale it vertically, which means we either stretch or shrink its vertical dimension. Practice the graphical and algebraic relationship of this transformation. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:scale/v/scaling-functions-horizontally 2022-10-06T23:23:50.639907812Z Scaling functions horizontally: examples The function f(k⋅x) is a horizontal scaling of f. See multiple examples of how we relate the two functions and their graphs, and determine the value of k. video https://cdn.kastatic.org/ka_thumbnails_cache/15301718-0526-4e35-b5a3-5f43c069aebe_1280_720_base.png Scaling functions horizontally: examples The function f(k⋅x) is a horizontal scaling of f. See multiple examples of how we relate the two functions and their graphs, and determine the value of k. https://cdn.kastatic.org/ka-youtube-converted/npMMbXm9sR0.mp4/npMMbXm9sR0.mp4 489 Scaling functions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:scale/v/compressing-functions-example 2021-06-30T17:32:37Z Identifying horizontal squash from graph Given the graphs of functions f and g, where g is the result of compressing f by a factor of 2, Sal finds g(x) in terms of f(x). video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Identifying horizontal squash from graph Given the graphs of functions f and g, where g is the result of compressing f by a factor of 2, Sal finds g(x) in terms of f(x). https://cdn.kastatic.org/ka-youtube-converted/4H5JZnytOfE.mp4/4H5JZnytOfE.mp4 196 Scaling functions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:scale/e/scale-functions-horizontally 2023-06-11T19:52:51.325539736Z Scale functions horizontally If we replace the input of a function with x multiplied by a constant, we scale it horizontally, which means we either stretch or shrink its horizontal dimension. Practice the graphical and algebraic relationship of this transformation. Tomer Gal exercise