Pre-Cal Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations.

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Presentation transcript:

Pre-Cal Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations

Definitions Transformations: operations that change the location, orientation, or size of a graph. Rigid Transformations: this type of transformation does not change the size or shape of the graph. It can move the graph horizontally, vertically, or reflect the graph about a given line. Non-Rigid Transformations: this type of transformation changes the shape of the graph. This could include stretching it horizontally and/or vertically.

Definitions Cont. Vertical Translation: this translation shifts the graph up or down in the coordinate plane. Horizontal Translation: this translation shifts the graph to the left or right in the coordinate plane.

Translations Cont. Vertical translations move the graph up or down using the following rules: y = f(x) + c moves the graph up c units y = f(x) – c moves the graph down c units

Translations Horizontal translations move the graph to the right or left using the following rules: y = f(x-c) translates the graph c units to the right. y = f(x+c) translates the graph c units to the left

Reflections Reflections across the x-axis keep the same x value but switch the y values. So if your coordinate is (-2,4), when you reflect it about the x-axis, your new coordinate would be (-2,-4). Reflections across the y-axis keep the y values the same but switch the x values. So if your coordinate is (4,-1), when you reflect it about the y-axis, your new coordinate would be (- 4,-1)

Reflections Cont. When you are completing the reflections for an actual graph of f(x) you need the follow the following rules: Across the x-axis: y = -f(x) Across the y-axis: y = f(-x)

Stretches Vertical shrink or stretch happens when you multiply by a number y = c f(x) A shrink occurs when the number you are multiplying by is < 1. So c < 1 A stretch occurs when the number you are multiplying by is > 1. So c > 1

Stretches Cont. A horizontal distortion takes place when you are dividing the x by some number(c). So y = f(x/c) A shrink occurs when c < 1. A stretch occurs when c > 1.