https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:absolute-value-piecewise-functions/x2f8bb11595b61c86:graphs-of-absolute-value-functions/v/shifting-absolute-value-graphs 2022-10-06T23:01:00.745424633Z Shifting absolute value graphs The graph of y=|x-h|+k is the graph of y=|x| shifted h units to the right and k units up. See worked examples practicing this relationship. video https://cdn.kastatic.org/ka_thumbnails_cache/791c6ac3-576d-4cff-af65-865b924ed152_1280_720_base.png Shifting absolute value graphs The graph of y=|x-h|+k is the graph of y=|x| shifted h units to the right and k units up. See worked examples practicing this relationship. https://cdn.kastatic.org/ka-youtube-converted/Wri26sPEBoI.mp4/Wri26sPEBoI.mp4 372 Graphs of absolute value functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:absolute-value-piecewise-functions/x2f8bb11595b61c86:graphs-of-absolute-value-functions/e/shift-absolute-value-graphs 2025-06-26T20:46:37.500606524Z Shift absolute value graphs y=|x-k|+h is the new equation of the absolute value function y=|x| shifted k units to the right and h units up. Practice this relationship between the graphical and algebraic representations of absolute value functions. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:absolute-value-piecewise-functions/x2f8bb11595b61c86:graphs-of-absolute-value-functions/v/reflecting-and-scaling-absolute-value-function 2021-07-03T04:45:02Z Scaling & reflecting absolute value functions: equation The graph of y=k|x| is the graph of y=|x| scaled by a factor of |k|. If k<0, it's also reflected (or "flipped") across the x-axis. In this worked example, we find the equation of an absolute value function from a description of the transformation performed on y=|x|. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Scaling & reflecting absolute value functions: equation The graph of y=k|x| is the graph of y=|x| scaled by a factor of |k|. If k<0, it's also reflected (or "flipped") across the x-axis. In this worked example, we find the equation of an absolute value function from a description of the transformation performed on y=|x|. https://cdn.kastatic.org/ka-youtube-converted/lPcahMeUYcU.mp4/lPcahMeUYcU.mp4 253 Graphs of absolute value functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:absolute-value-piecewise-functions/x2f8bb11595b61c86:graphs-of-absolute-value-functions/v/scaling-and-reflecting-absolute-value-graphs 2022-10-06T23:01:00.745424633Z Scaling & reflecting absolute value functions: graph The graph of y=k|x| is the graph of y=|x| scaled by a factor of |k|. If k<0, it's also reflected (or "flipped") across the x-axis. In this worked example, we find the equation of an absolute value function from its graph. video https://cdn.kastatic.org/ka_thumbnails_cache/5d15ba36-d5c2-405b-a0dd-f52d69086a6f_1280_720_base.png Scaling & reflecting absolute value functions: graph The graph of y=k|x| is the graph of y=|x| scaled by a factor of |k|. If k<0, it's also reflected (or "flipped") across the x-axis. In this worked example, we find the equation of an absolute value function from its graph. https://cdn.kastatic.org/ka-youtube-converted/Yyfk0rwuZSE.mp4/Yyfk0rwuZSE.mp4 208 Graphs of absolute value functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:absolute-value-piecewise-functions/x2f8bb11595b61c86:graphs-of-absolute-value-functions/e/stretch-and-shrink-absolute-value-graphs 2026-05-12T22:10:47.015864082Z Scale & reflect absolute value graphs y=a|x| is a stretched/shrunk version of the absolute value function y=|x|. Practice this relationship between the graphical and algebraic representations of absolute value functions. 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 Graphs of absolute value functions 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/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