2.6 Translations and Families of Functions

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Presentation transcript:

2.6 Translations and Families of Functions

Parent Function – the simplest form in a set of functions that form a family Each function in the family is a transformation of the parent function. Translation – one type of transformation, Shifts the graph of the parent function horizontally, vertically, or both without changing shape or orientation.

Vertical Translation

EX: Translate up 5 units.

How are y = 2x and y = 2x – 3 related? EX: How are y = 2x and y = 2x – 3 related? What is the graph of translated up 2 units?

Horizontal Translation

EX: Describe the translation.

EX: Write the equation for the given graph:

Write the equation of the graph below.

Reflections: Flips the graph across a line, such as the x or y-axis. f(-x) reflects over the y-axis The x value changes sign -f(x) reflects over the x-axis The y value changes sign

EX: Given x y Find f(-x) and –f(x) and sketch. 1 1 3 4 5 1

If looks like Graph Graph

Vertical Stretch – multiplies all y-values by a factor of a > 1 Vertical Compression (shrink) – reduces all y-values by the same factor between 0 and 1. 0 < a <1

EX: Given f(x) = x y Find 3f(x) and f(x) and sketch. -5 2. -2 2. 0 -3

EX: Write the equation for the following statement: The graph of g(x) is the graph of f(x) = reflected in the y-axis, left 7 units and shifted down 3 units.

EX: What transformations change the graph of