what is the correct order of transformations

by Prof. Polly Krajcik II Published 3 years ago Updated 3 years ago

What is the correct order of transformations?

Start with parentheses (look for possible horizontal shift) (This could be a vertical shift if the power of x is not 1.)
Deal with multiplication (stretch or compression)
Deal with negation (reflection)
Deal with addition/subtraction (vertical shift)

Part of a video titled Transformation Correct Order - YouTube

0:34

7:47

You can write horizontal translation first and then vertical. Or you can do vertical translationMoreYou can write horizontal translation first and then vertical. Or you can do vertical translation first and then horizontal. And on the other hand you can do vertical stretches.

Full Answer

What is the sequence of transformation?

Question 1 SURVEY 30 seconds Q. ...
Question 2 SURVEY 60 seconds Q. ...
Question 3 SURVEY 300 seconds Q. ...
Question 4 SURVEY 30 seconds Q. ...
Question 5 SURVEY 30 seconds Q. ...
Question 6 SURVEY 60 seconds Q. ...
Question 7 SURVEY 120 seconds Q. ...
Question 8 SURVEY 60 seconds Q. ...
Question 9 SURVEY 30 seconds Q. ...
Question 10 SURVEY 300 seconds Q. ...

More items...

What is the best transformation?

What Is The Best Beginner Transformation Workout?

Stay hydrated. Drink 1-2 gallons of water per day.
Aim for 1g/lb of protein daily to repair and build new tissue.
Consume at least 25g of fiber daily. Fiber is necessary for digestive system health and function.
Eat more fruits and vegetables daily. ...

What are the rules of transformation graphs?

Transformations

Translations. A translation is a sliding of a figure. ...
Rotations. A second type of transformation is the rotation . ...
Reflections. A third type of transformation is the reflection . ...
Dilations. A dilation is a transformation which preserves the shape and orientation of the figure, but changes its size.

What are transformation rules?

Transformation Rules

You use the Manage Product Transformation Rules page in the Setup and Maintenance work area to write the transformation rule. ...
You can't use a transformation rule to add a product model to a sales order.
An order line that a transformation rule creates gets most attributes from the line that the rule uses to create the new line. ...

What is an example of a sequence of transformations?

An example of a sequence of transformations is when more than one transformation occurs. This could be a reflection over the x-axis then a rotation...

How do you identify a transformation from a graph?

Identify a transformation on a graph by first identifying what transformation is happening. A translation is a slide on a graph, a reflection is a...

What are the four types of transformations in math?

The four types of transformations in math are the reflection, rotation, translation, and dilation. A reflection is a flip, a rotation is a turn, a...

How do you find the transformation sequence?

Find the transformation sequence by first describing the first transformation. If the first transformation is a turn then the sequence starts with...

Rotation

A rotation is a turn around a center point. In a rotation, the distance from each point on the shape to the center remains the same. A rotation is identified by a shape turning a specific amount degrees, usually 90, 180, or 270 degrees, around a point either clockwise or counterclockwise.

Reflection

A reflection is a transformation where every point is the same distance from the center line. A reflection is also called a flip or a mirror image. It is congruent to the pre-image and the only thing needed to calculate a reflection is the line of reflection.

Translation

A translation is a transformation where a figure is being moved. Translations are also called a slide because the shape is being slid across a graph. The shape is congruent and each point is moved the exact same amount to get the image.

Dilation

A dilation is the resizing of a figure. For this transformation, the pre-image and image are similar to each other, not congruent. Each side length is enlarged or reduced by the same proportion to keep the shape the same without having the same lengths. For an enlargement, the dilation is a value greater than 1.

What has Ozgur learned about transformations?

Ozgur has learned about each individual transformation (respectively, vertical and horizontal reflections, vertical and horizontal stretches or shrinks, and vertical and horizontal shifts); but now wants to be able to read a function and determine the correct sequence of transformations. Which comes first? (And the example he gives is the hardest case.)

How to do the shift and shrink?

If instead we first do the shift, changing f (x) to f (x+b), and THEN do the shrink, we replace x in x+b with ax, and get f (ax+b), which is what we want. So that is one answer: Start with: f (x) Shift b units to the left: f (x+b) Shrink horizontally by a factor of a: f (ax+b)

What is the stretch first method?

The stretch-first method is based on rewriting the function as . We first stretch by a factor of 2, then shift right by 2 units:

Is "this MUST be seen as replacing the x itself with a negative, multiple or sum" correct?

Aha! You are absolutely correct. [of course :) ] I was improperly applying the transformation. Your key phrase "This MUST be seen as REPLACING the x itself with a negative, multiple or sum" cleared it up for me. Thank you for your time and clear explanation!

Can we do two transformations in the same order?

But in fact we COULD do the two transformations in the other order, if we change the particular amounts. We can write f (ax+b) as f (a (x+b/a)), factoring out the a, and then do this: Start with: f (x) Shrink horizontally by a factor of a: f (ax) Shift b/a units to the left: f (a (x+b/a)) = f (ax+b)

Why do you scale first and rotate?

The reason is because usually you want the scaling to happen along the axis of the object and rotation about the center of the object.

Can you calculate Mandelbrot coordinates from screen coordinates?

Note that you need to calculate Mandelbrot coordinates from screen coordinates and not the other way around. This is to ensure that you evaluate the Manderbrot equation for each pixel exactly once and are not left with holes in the image or do double evaluation per pixel.

How to scale a CF?

cf (bx+a)+d = Translate by a units in the negative X direction, then scale by a factor of 1/b parallel to the X-axis, then scale by a factor of c parallel to the Y-axis, then translate by d units in the positive Y direction.

How to scale a point to the X axis?

So scale parallel to the X axis by a factor of 1/2, then move left by 2 units. Hence, the original point becomes x= (8/2)-2 = 2

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