Transformations Translations, Reflections, Rotations Calculator

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Example

Created on 2024-06-20Asked by Harper Adams (Solvelet student)

Perform the following transformations on the function

f(x) = \sqrt{x}

: 1. Translate 3 units to the right. 2. Reflect across the

x

-axis. 3. Rotate 90 degrees counterclockwise about the origin.

Solution

Given the function

f(x) = \sqrt{x}

, let's perform each transformation: 1. **Translate 3 units to the right:** The transformed function

f_1(x)

is obtained by replacing

x

with

x - 3

f(x)

f_1(x) = \sqrt{x - 3}.

2. **Reflect across the

x

-axis:** The reflected function

f_2(x)

is obtained by replacing

f(x)

with

-f(x)

f_2(x) = -\sqrt{x}.

3. **Rotate 90 degrees counterclockwise about the origin:** The rotated function

f_3(x)

is obtained by replacing

x

with

y

and

y

with

-x

f(x)

f_3(x) = \sqrt{-x}.

Solved on Solvelet with Basic AI Model

Some of the related questions asked by Logan King on Solvelet

1. Perform the following transformations on the point

P(2,3)

: a) Translate

3

units to the right and

2

units up. b) Reflect across the

x

-axis. c) Rotate

90

degrees counterclockwise about the origin.2. Given the transformation matrix

\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}

, perform a rotation of 90° counterclockwise on the point

P(4, -3)

DefinitionTransformation alters the shape's situation, course, or scope Translations move a shape without changing the size, Reflections flip it over a line, and Rotations turn a shape around a point. Now for Example take a point (2,3) translating this point by (4,-2) will gives (6,1) reflecting this point about y-axis will gives (-2,3) rotating this point 90° counterclockwise about the origin will give us (-3,2)

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