Difference between revisions of "Multiple Transformations of Functions"
(Created page with "See Single Transformations of Functions ==Resources== * [https://online.math.uh.edu/Math1330-unpaid/ch1/s13/CombTransf/Combining_Transformations_Math1330_s13.pdf Combining...") |
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| − | See [[Single Transformations of Functions]] | + | See [[Single Transformations of Functions]] for more information on translating, reflecting, compressing, and stretching functions. |
| + | ==Combining Functions== | ||
| + | ===Combining vertical and horizontal shifts=== | ||
| + | [[File:Two shifts.png|thumb|Vertical and horizontal shift: f(x) = x^2 + x (red) and g(x) = (x - 3)^2 + (x - 3) + 5 (blue; f(x) shifted 3 units right and 5 units up)]] | ||
| + | If <math> f(x) </math> is some function, then <math> g(x) = f(x - h) + k </math> is the function <math> f(x) </math> shifted h units horizontally (to the right for h > 0 and to the left for h < 0) and k units vertically (up for k > 0 and down for k < 0). For example, <math> g(x) = (x - 3)^2 + (x - 3) + 5 </math> is the function <math> f(x) = x^2 + x </math> shifted 3 units to the right and 5 units up. <math> g(x) = \sqrt{x + 2} - 6 </math> is the function <math> f(x) = \sqrt{x} </math> shifted 2 units to the left and 6 units down. | ||
| + | |||
==Resources== | ==Resources== | ||
* [https://online.math.uh.edu/Math1330-unpaid/ch1/s13/CombTransf/Combining_Transformations_Math1330_s13.pdf Combining Transformations], University of Houston | * [https://online.math.uh.edu/Math1330-unpaid/ch1/s13/CombTransf/Combining_Transformations_Math1330_s13.pdf Combining Transformations], University of Houston | ||
* [https://courses.lumenlearning.com/waymakercollegealgebra/chapter/sequences-of-transformations/ Sequences of Transformations], Lumen Learning | * [https://courses.lumenlearning.com/waymakercollegealgebra/chapter/sequences-of-transformations/ Sequences of Transformations], Lumen Learning | ||
Revision as of 14:17, 16 September 2021
See Single Transformations of Functions for more information on translating, reflecting, compressing, and stretching functions.
Combining Functions
Combining vertical and horizontal shifts
If 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 f(x) } is some function, then 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) + k } is the 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 f(x) } shifted h units horizontally (to the right for h > 0 and to the left for h < 0) and k units vertically (up for k > 0 and down for k < 0). For example, 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) = (x - 3)^2 + (x - 3) + 5 } is the 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 f(x) = x^2 + x } shifted 3 units to the right and 5 units up. 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) = \sqrt{x + 2} - 6 } is the 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 f(x) = \sqrt{x} } shifted 2 units to the left and 6 units down.
Resources
- Combining Transformations, University of Houston
- Sequences of Transformations, Lumen Learning
