Difference between revisions of "Single Transformations of Functions"
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==Introduction== | ==Introduction== | ||
| − | One kind of transformation involves shifting the entire graph of a function up, down, right, or left. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. In other words, we add the same constant to the output value of the function regardless of the input. For a function g(x) = f(x) + k, the function f(x) is shifted vertically k units. For example, <math> g(x) = x^2 + 4 </math> is the function <math> f(x) = x^2 </math> shifted up by 4 units. | + | One kind of transformation involves shifting the entire graph of a function up, down, right, or left. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. In other words, we add the same constant to the output value of the function regardless of the input. For a function <math> g(x) = f(x) + k </math>, the function <math> f(x) </math> is shifted vertically k units. For example, <math> g(x) = x^2 + 4 </math> is the function <math> f(x) = x^2 </math> shifted up by 4 units. <math> g(x) = sin(x) - 7.7 </math> is the function <math> f(x) = sin(x) </math> shifted down by 7.7 units. |
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| + | Given a function f, a new function <math> g(x) = f(x − h) </math>, where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift h units to the right. If h is negative, the graph will shift h units to the left. For example, <math> g(x) = (x - 3)^2 </math> is the graph of <math> f(x) = x^2 </math> shifted 3 units to the right. <math> g(x) = sin(x + \frac{\pi}{2}) </math> is the function <math> f(x) = sin(x) </math> shifted <math> \frac{\pi}{2} units </math> to the left. | ||
==Resources== | ==Resources== | ||
* [https://courses.lumenlearning.com/wmopen-collegealgebra/chapter/introduction-transformations-of-functions/ Intro to Transformations of Functions], Lumen Learning | * [https://courses.lumenlearning.com/wmopen-collegealgebra/chapter/introduction-transformations-of-functions/ Intro to Transformations of Functions], Lumen Learning | ||
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Revision as of 17:20, 15 September 2021
Introduction
One kind of transformation involves shifting the entire graph of a function up, down, right, or left. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. In other words, we add the same constant to the output value of the function regardless of the input. For a function , the function is shifted vertically k units. For example, is the function shifted up by 4 units. is the function shifted down by 7.7 units.
Given a function f, a new function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g(x) = f(x − h) } , where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift h units to the right. If h is negative, the graph will shift h units to the left. For example, is the graph of shifted 3 units to the right. is the function shifted to the left.
Resources
- Intro to Transformations of Functions, Lumen Learning
