1. 2.6 Translations and Families of Functions

2. 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.

3. Vertical Translation

4. EX: Translate up 5 units.

5. 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?

6. Horizontal Translation

7. EX: Describe the translation.

8. EX: Write the equation for the given graph:

9. Write the equation of the graph below.

10. 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

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

12. If looks like
Graph
Graph

13. 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 < a <1

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

16. 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.

17. EX: What transformations change the graph of