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Vertical and Horizontal Transformations

Shifts of parent functions produced by adding a constant term.

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Transforming Functions

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Vocabulary

Word Definition
____________ Also called translation or slide; a transformation applied to the graph of a function which does not change the shape of the graph, only the location
____________ a result of adding a constant term to the value of a function; moves up or down
Horizontal Shift _________________________________________________________________

Reflection

_________________________________________________________________
____________ transformation which results in the width of a graph being increased or decreased; the result of the co-efficient of the term being between 0 and 1.
Compression _________________________________________________________________

What transformations must be applied to  , in order to graph  ?

Practice

Answer the following questions:
  1. If a function is multiplied by a coefficient, what will happen to the graph of the function?
  2. What does multiplying x by a number greater than one create?
  3. What happens when we multiply x by a number between 0 and 1
  4. In order to obtain a reflection over the y axis what do we have to do to x?
  5. How do we obtain a reflection over the x-axis?
  6. Write a function that will create a horizontal compression of the following: 
  7. Write a function that will horizontally stretch the following: 
  8. Rewrite this function  to get a reflection over the x-axis.
  9. Rewrite this function  to get a reflection over the y-axis.
Graph each of the following using transformations. Identify which transformations are used.
Answer the following questions:
  1. What part of the function  shifts the graph of vertically?
  2. What part of the function  reflects the graph of  across the x-axis?
  3. What is different between the functions  and  that changes the appearance of the graph?
  4. Write a function  whose graph looks like the graph of  reflected across the x-axis and shifted up 1 unit. 
  5. How do you transform the graph of:  so that it looks like the graph of: 
    1. Stretch it by a factor of ¼ and shift it up 6 units. 
    2. Stretch it by a factor of 6 and shift it left 4 units. 
    3. Stretch it by a factor of 4 and shift it down 6 units. 
    4. Stretch it by a factor of 4 and shift it up 6 units.

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