Rules For Transformations Math

We added a 3 outside the basic squaring function f x x2 and thereby went from the basic quadratic x2 to the transformed function x2 3.

Rules for transformations math. Reflection a reflection is an isometry in which the preimage and the image have opposite orientations. X y x y over the y axis. X y x y. Types of transformations in math.

Translation a translation or slide is an isometry in which all points of a figure move the same distance and in the same direction. Reflection about the x x axis given the graph of f x f x then the graph of g x f x g x f x is the graph of f x f x reflected about the x x axis. Learn about t ransformations of function rules transformations of quadratic functions types of transformations transformations definition and transformations algebra in the concept of transformations. W x x3 4x 3.

Common rotations about the origin. There are basically four types of transformations. W x x 5 3 4 x 5 graph. This is always true.

The flip is performed over the line of reflection lines of symmetry are examples of lines of reflection. 90º r x y y x clockwise. W x 3x 3 4 3x 27x3 12x. Move 3 spaces down.

Compress it by 3 in the x direction. That is x2 3 is f x 3. These are basic rules which are followed in this concept. W x 2 x3 4x 2x3 8x.

When rotating a point 270 degrees counterclockwise about the origin our point a x y becomes a y x. To determine the image point when performing reflections rotations translations and dilations use the following rules. Reflections are isometric but do not preserve orientation. In coordinate geometry problems there are special rules for certain types of transformations.

Move 4 spaces right. This means we switch x and y and make x negative. Move 2 spaces up. Reflections are a flip.

F x b is f x moved up b units. 4 5 5 4 ex 4 5 5 4 180º r x y x y. W x x 4 3 4 x 4 move 5 spaces left. Transformations could be rigid where the shape or size of preimage is not changed and non rigid where the size is changed but the shape remains the same.

To move a function up you add outside the function. Check out the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page. The final set of transformations that we re going to be looking at in this section aren t shifts but instead they are called reflections and there are two of them. Stretch it by 2 in the y direction.