does the order of translations matter ?

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does the order of translations matter ?

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https://math.stackexchange.com/questions/4269230/does-the-order-of-graph-transformations-matter

https://math.stackexchange.com/questions/4269230/does-the-order-of-graph-transformations-matter
Does the order of graph transformations matter?
as required. Rule of thumb: start with the innermost transformation and work outwards. Generally order does not matter if the transformations consist only of translations or only of enlargements. But if there are translations and enlargements in the same axis direction, then order matters.
In which order do I graph transformations of functions?
Scale (Stretch or shrink) Vertical or horizontal order do not matter. Reflect Vertical or horizontal order do not matter. Shift Vertical or horizontal order do not matter. Share. Cite. Follow answered Feb 20, 2018 at 17:06. Jake Rodriguez Jake Rodriguez. 9 $endgroup$ Add a …
geometrical transformation order – Mathematics Stack Exchange
In a general case the order of transformations is important. In the following picture the red triangle is first translated by vector AA′→ A A ′ → and then reflected with respect to line p p (brown triangles). You get a different result if you first reflect and then translate (blue triangles). However, there is a special case when the …
What is the correct order of transformations scale, rotate and …
When applying rotate (about origin), scale (in which we shall translate towards origin and then back) and translate, does it matter in what order we do it? Why? Basically in my case I have an image in coordinate space that goes from -2 to +2 in x and -1.5 to +1.5 in y to get ration of 4:3.

https://mathbitsnotebook.com/Algebra2/FunctionGraphs/FGCompositeTransformations.html

https://mathbitsnotebook.com/Algebra2/FunctionGraphs/FGCompositeTransformations.html
Sequence of Transformations on Functions – MathBitsNotebook(A2)
Consider the problem f (x) = 2(x + 3) – 1. The parent function is f (x) = x, a straight line. It can be seen that the parentheses of the function have been replaced by x + 3, as in f (x + 3) = x + 3. This is a horizontal shift of three units to the left from the parent function.. The multiplication of 2 indicates a vertical stretch of 2, which will cause to line to rise twice as fast as the …

https://www.themathdoctors.org / combining-function-transformations-order-matters

https://www.themathdoctors.org / combining-function-transformations-order-matters
Combining Function Transformations: Order Matters
Transformations like a+bf(x) (vertical shifts and stretches) are done in the SAME order as the order of operations. Also, these do not interact with the horizontal transformations, so it doesn’t matter which order you do them in; if you had, say, af(bx) you could do the vertical stretch followed by the horizontal shrink, or vice versa. Try it …

https://courses.lumenlearning.com/waymakercollegealgebra/chapter/sequences-of-transformations

https://courses.lumenlearning.com/waymakercollegealgebra/chapter/sequences-of-transformations
Sequences of Transformations | College Algebra – Lumen Learning
Combine Shifts and Stretches. When combining transformations, it is very important to consider the order of the transformations. For example, vertically shifting by 3 and then vertically stretching by 2 does not create the same graph as vertically stretching by 2 and then vertically shifting by 3, because when we shift first, both the original function and the shift get stretched, while only …

https://www.nagwa.com/en/explainers/707102751905

https://www.nagwa.com/en/explainers/707102751905
Lesson Explainer: Function Transformations: Translations | Nagwa
The order in which we apply the vertical and horizontal shifts does not matter, since either order will lead to the same result in the end. In the next example, we will find the coordinates of a corresponding point on the graph of a function obtained by translating the graph of a given function both horizontally and vertically.

https://online.math.uh.edu/Math1330-unpaid/ch1/s13/CombTransf/Combining_Transformations_Math1330_s13.pdf

https://online.math.uh.edu/Math1330-unpaid/ch1/s13/CombTransf/Combining_Transformations_Math1330_s13.pdf
PDF Math 1330 – Combining Transformations – University of Houston
this problem. In this particular example, the order does matter, and we could get an incorrect graph if we perform certain operations out of order. (There are other cases where the order does not matter, depending on which transformations are used.) It is worth spending some time analyzing the order of transformations – which can be done

https://math.libretexts.org/Bookshelves/Precalculus/Active_Prelude_to_Calculus_(Boelkins)/01:_Relating_Changing_Quantities/1.08:_Transformations_of_Functions

https://math.libretexts.org/Bookshelves/Precalculus/Active_Prelude_to_Calculus_(Boelkins)/01:_Relating_Changing_Quantities/1.08:_Transformations_of_Functions
1.8: Transformations of Functions – Mathematics LibreTexts
In Figure (PageIndex{3}), we see a horizontal translation of the original function (f) that shifts its graph (2) units to the right to form the function (htext{.})Observe that (f) is not a familiar basic function; transformations may be applied to any original function we desire. From an algebraic point of view, horizontal are slightly more complicated than vertical ones.

https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-8-for-ccss/section/1.11/related/lesson/order-of-composite-transformations-alg-i-hnrs

https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-8-for-ccss/section/1.11/related/lesson/order-of-composite-transformations-alg-i-hnrs
Order of Composite Transformations
29 nov. 2023Therefore order does matter. Example 4. The triangle with vertices J (− 5, − 2), K (− 1, 4) and L (1, − 3) has undergone a transformation of up 4 and over to the right 4 and then a reflection in the x-axis. Draw and label the composite transformation. Does order matter? Order: Translation then Reflection. : Reflection then …

https://mathbitsnotebook.com/Geometry/Transformations/TRCompositeTransformations.html

https://mathbitsnotebook.com/Geometry/Transformations/TRCompositeTransformations.html
Composition of Transformations (Isometries) – MathBitsNotebook(Geo)
The symbol for a composition of transformations (or functions) is an open circle. A notation such as is read as: a translation of ( x, y) → ( x + 1, y + 5) after a reflection in the line y = x. You may also see the notation written as . This process must be done from right to left ()!! Composition of transformations is not commutative.

https://undergroundmathematics.org/combining-functions/order-order/solution

https://undergroundmathematics.org/combining-functions/order-order/solution
Solution | Order! Order! | Combining Functions | Underground Mathematics
Applying (2) then (1) translates it down then left. The result is the same; the order does not matter. One of the key points on the graph is the local maximum at ((0,4)). Applying the transformations in either order takes this point to ((-2,0)) as shown dotted in the diagram.
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