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Function Transformations

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Essential Functions

  • Sketch each of the following:
    • What is the domain, range, intercepts?
  • Constant
  • Line
  • Parabola
  • Cubic
  • Reciprocal
  • Square Root
  • Exponential
  • Absolute Value

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Composition

  • Each person in the group pick a different function
  • Consider a line
  • Compose this function with a line

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  • Have the line composed with the function

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  • Describe the qualitative result using specific Desmos sliders
  • What is happening?

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How to track this

  • Make a table of different p, q values and see the effects of each composition on the function
  • The vertical transformations seem to match up with our intuition
  • Horizontal transformations seem to be the exact opposite of our intuition

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Vertical Transformations

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  • a: vertical stretch, vertical compression, vertical reflection
  • k: vertical shift
  • a>1 vert str
  • 0<a<1 vert compr
  • a<0 reflection (with stretch or compression)
  • k>0 shift up
  • k<0 shift down

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Horizontal

Transformations

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  • b horizontal stretch, horizontal compression, horizontal reflection
  • h horizontal shift
  • b>1 horiz compr
  • 0<b<1 horiz str
  • b<0 reflection (with stretch or compression)
  • h>0 shift right
  • h<0 shift left

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Examples

  • Graph the function by transforming an appropriate base graph
  • Determine the domain, range, intercepts

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Examples

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Examples

  • Graph the function by transforming an appropriate base graph
  • Determine the domain, range, intercepts

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Examples

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Examples

  • Graph the function by transforming an appropriate base graph
  • Determine the domain, range, intercepts

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Examples

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Examples

  • Graph the function by transforming an appropriate base graph
  • Determine the domain, range, intercepts, asymptotes

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Examples

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Examples

  • Graph the function by transforming an appropriate base graph
  • Determine the domain, range, intercepts, asymptotes

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Examples

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