Transforming Graphs Of Functions
Gbogbo ọrọ náà
If you know the graph of a function, you can get the graph of a related function by sliding it around, without plotting it again. Recognising these transformations lets you sketch a whole family of graphs from one you already know.
In this lesson you will describe and identify transformations of the graph of \(y = f(x)\): a vertical translation \(y = f(x) + k\) and a horizontal translation \(y = f(x + k)\).
Ebumnobi
- Describe and identify transformations to a graph of y = f(x) when y = f(x) + k or y = f(x + k).
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Ekele diri gi maka imecha ihe karịrị na Transforming Graphs Of Functions. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- The graph of y = f(x) + 2 is y = f(x): A. moved up 2 B. moved down 2 C. moved right 2 D. moved left 2 Answer: A
- The graph of y = f(x + 3) is y = f(x): A. moved up 3 B. moved right 3 C. moved left 3 D. moved down 3 Answer: C
- If f(x) = x^2, the vertex of y = f(x) + 2 is at: A. (0, 0) B. (0, 2) C. (2, 0) D. (-2, 0) Answer: B
- If f(x) = x^2, the vertex of y = f(x + 3) is at: A. (3, 0) B. (-3, 0) C. (0, 3) D. (0, -3) Answer: B
- A translation changes a graph's: A. shape B. position C. steepness D. width Answer: B
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Transformation of Functions
Graph functions using vertical and horizontal shifts.
"Algebra and Trigonometry: Transformation of Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/3-5-transformation-of-functions. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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