Upcoming SlideShare
×

2.6

1,192 views
1,091 views

Published on

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Be the first to comment

• Be the first to like this

Views
Total views
1,192
On SlideShare
0
From Embeds
0
Number of Embeds
25
Actions
Shares
0
10
0
Likes
0
Embeds 0
No embeds

No notes for slide
• These notes were made using the textbook and “reteaching”
• 2.6

1. 1. 2.6 FAMILIES OF FUNCTIONS
2. 2. FAMILIES OF FUNCTIONS <ul><li>There are sets of functions, called families that share certain characteristics. </li></ul><ul><ul><li>A parent function is the simplest form in a set of functions that form a family. </li></ul></ul><ul><ul><li>Each function in the family is a transformation of the parent function </li></ul></ul>
3. 3. FAMILIES OF FUNCTIONS
4. 4. TRANSLATIONS <ul><li>One type of transformation is a translation . </li></ul><ul><ul><li>A translation shifts the graph of the parent function horizontally, vertically, or both without changing shape or orientation. </li></ul></ul>
5. 6. EXAMPLE <ul><li>How can you represent each translation of y = |x| graphically? </li></ul>Shift the parent graph down 2 units Shift the parent graph left 1 unit
6. 7. EXAMPLE <ul><li>How can you represent each translation of y = |x| graphically? </li></ul>Shift the parent graph right 3 units and up 1 units Shift the parent graph left 2 units and down 3 units
7. 8. REFLECTIONS <ul><li>A reflection flips the graph over a line (such as the x – or y – axis) </li></ul><ul><ul><li>Each point on the graph of the reflected function is the same distance from the line of reflection as its corresponding point on the graph of the original function. </li></ul></ul>
8. 9. REFLECTIONS When you reflect a graph in the y-axis, the x values change signs and the y-values stay the same. When you reflect a graph in the x-axis, the y-values change signs and the x-values stay the same.
9. 11. REFLECTING A FUNCTION ALGEBRAICALLY <ul><li>Let and be the reflection in the x-axis. What is a function rule for ? </li></ul>
10. 12. REFLECTING A FUNCTION ALGEBRAICALLY <ul><li>Let and be the reflection in the </li></ul><ul><li> y-axis. What is a function rule for ? </li></ul>
11. 13. 2.6 CONTINUED
12. 14. VERTICAL STRETCH AND VERTICAL COMPRESSION <ul><li>A vertical stretch multiplies all y-values of a function by the same factor greater than 1. </li></ul><ul><li>A vertical compression reduces all </li></ul><ul><li>y-values of a function by the same factor between 0 and 1. </li></ul>Why do you think the value being multiplied is always positive?
13. 16. EXAMPLE <ul><li>The table represents the function f(x). Complete the table to find the vertical stretch and vertical compression. Then graph the functions. </li></ul>
14. 18. EXAMPLE: COMBINING TRANSFORMATIONS <ul><li>The graph of g(x) is the graph of f(x) = 4x compressed vertically by the factor ½ and then reflected in the y-axis. What is the function rule for g(x)? </li></ul>
15. 19. EXAMPLE: COMBINING TRANSFORMATIONS <ul><li>The graph of g(x) is the graph of f(x) = x stretched vertically by the factor 2 and then translated down 3 units. What is the function rule for g(x)? </li></ul>
16. 20. EXAMPLE: COMBINING TRANSFORMATIONS <ul><li>What transformations change the graph of f(x) to the graph of g(x)? </li></ul>