2.6 FAMILIES OF FUNCTIONS
FAMILIES OF FUNCTIONS <ul><li>There are sets of functions, called  families  that share certain characteristics. </li></ul...
FAMILIES OF FUNCTIONS
TRANSLATIONS <ul><li>One type of transformation is a  translation . </li></ul><ul><ul><li>A  translation  shifts the graph...
 
EXAMPLE <ul><li>How can you represent each translation of y = |x| graphically? </li></ul>Shift the parent graph  down 2 un...
EXAMPLE <ul><li>How can you represent each translation of y = |x| graphically? </li></ul>Shift the parent graph right 3 un...
REFLECTIONS <ul><li>A  reflection  flips the graph over a line (such as the x – or y – axis) </li></ul><ul><ul><li>Each po...
REFLECTIONS When you reflect a graph in the y-axis, the x values change signs and the y-values stay the same. When you ref...
 
REFLECTING A FUNCTION ALGEBRAICALLY <ul><li>Let    and be the reflection in the x-axis. What is a function rule for ?  </l...
REFLECTING A FUNCTION ALGEBRAICALLY <ul><li>Let    and   be the reflection in the </li></ul><ul><li>  y-axis. What is a fu...
2.6 CONTINUED
VERTICAL STRETCH AND  VERTICAL COMPRESSION <ul><li>A  vertical stretch  multiplies all y-values of a function by the same ...
 
EXAMPLE <ul><li>The table represents the function f(x). Complete the table to find the vertical stretch and vertical compr...
 
EXAMPLE: COMBINING TRANSFORMATIONS <ul><li>The graph of g(x) is the graph of f(x) = 4x compressed vertically by the factor...
EXAMPLE: COMBINING TRANSFORMATIONS <ul><li>The graph of g(x) is the graph of f(x) = x stretched vertically by the factor 2...
EXAMPLE: COMBINING TRANSFORMATIONS <ul><li>What transformations change the graph of f(x) to the graph of g(x)? </li></ul>
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  • Transcript of "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>
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