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Combining Transformations

Order of shifts, stretches, compressions, and reflections of a parent function.

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Transforming Functions

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 y=x2 , in order to graph g(x)=3(x4)2+2 ?

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: f(x)=x2+3
  7. Write a function that will horizontally stretch the following: f(x)=x26
  8. Rewrite this function f(x)=x to get a reflection over the x-axis.
  9. Rewrite this function f(x)=x to get a reflection over the y-axis.
Graph each of the following using transformations. Identify which transformations are used.
  1. f(x)=|x3|+4
  2. h(x)=x+7
  3. g(x)=1x5
  4. f(x)=3x3
  5. h(x)=(x7)3+4
  6. f(x)=14(x9)2+5
  7. f(x)=3x+26
  8. f(x)=34(x+5)+45
Answer the following questions:
  1. What part of the function g(x)=(f(x)+1)=(x3+1) shifts the graph of f(x)vertically?
  2. What part of the function g(x)=(f(x)+1) reflects the graph of f(x) across the x-axis?
  3. What is different between the functions g(x)=(x3+1.0) and h(x)=x3+1.0 that changes the appearance of the graph?
  4. Write a function g(x) whose graph looks like the graph of f(x)=|x| reflected across the x-axis and shifted up 1 unit. g(x)=
  5. How do you transform the graph of: f(x)=x3 so that it looks like the graph of:f(x)=4x3+6 
    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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