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  • These notes were made using the textbook and “reteaching”

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  • 1. 2.6 FAMILIES OFFUNCTIONS
  • 2. FAMILIES OF FUNCTIONS There are sets of functions, called families that share certain characteristics. A parent function is the simplest form in a set of functions that form a family.  Each function in the family is a transformation of the parent function
  • 3. FAMILIES OF FUNCTIONS
  • 4. TRANSLATIONS One type of transformation is a translation. A translation shifts the graph of the parent function horizontally, vertically, or both without changing shape or orientation.
  • 5. EXAMPLE How can you represent each translation of graphically?1. Shift the parent graph down 2 units2. Shift the parent graph left 1 unit
  • 6. EXAMPLE How can you represent each translation of graphically?1.Shift the parent graph right 3units and up 1 units2. Shift the parent graph left 2 units and down 3 units
  • 7. REFLECTIONS A reflection flips the graph over a line (such as the x – or y – axis)  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.
  • 8. When you reflect a graphREFLECTIONS 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. REFLECTING A FUNCTIONALGEBRAICALLY ( )Let f x = 3 x + 3 ( ) and g x be the reflection ( )in the x-axis. What is a function rule for g x ? g ( x) = − f ( x)
  • 10. REFLECTING A FUNCTIONALGEBRAICALLY ( ) ( )Let f x = 3 x + 3 and g x be the reflection in the ( )y-axis. What is a function rule for g x ? g ( x) = f ( −x)
  • 11. VERTICAL STRETCH ANDVERTICAL COMPRESSION A vertical stretch multiplies all y-values of a function by the same factor greater than 1. A vertical compression reduces all y-values of a function by the same factor between 0 and 1.Why do you think the value being multiplied isalways positive?
  • 12. EXAMPLEThe table represents the function f(x). Completethe table to find the vertical stretch and verticalcompression. Then graph the functions.
  • 13. EXAMPLE: COMBININGTRANSFORMATIONSThe graph of g(x) is the graph of f(x) = 4xcompressed vertically by the factor ½ and thenreflected in the y-axis. What is the function rulefor g(x)?
  • 14. EXAMPLE: COMBININGTRANSFORMATIONSThe graph of g(x) is the graph of f(x) = x stretchedvertically by the factor 2 and then translateddown 3 units. What is the function rule for g(x)?
  • 15. HOMEWORK 2.6 Worksheet