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 
_________________________________________________________________ 
____________  A transformation which results in the width of a graph being increased or decreased; the result of the coefficient of the x term being between 0 and 1. 
Compression  _________________________________________________________________ 
What transformations must be applied to
Practice
Answer the following questions:
 If a function is multiplied by a coefficient, what will happen to the graph of the function?
 What does multiplying x by a number greater than one create?
 What happens when we multiply x by a number between 0 and 1
 In order to obtain a reflection over the y axis what do we have to do to x?
 How do we obtain a reflection over the xaxis?
 Write a function that will create a horizontal compression of the following:
f(x)=x2+3  Write a function that will horizontally stretch the following:
f(x)=x2−6  Rewrite this function
f(x)=−x√ to get a reflection over the xaxis.  Rewrite this function
f(x)=x√ to get a reflection over the yaxis.
Graph each of the following using transformations. Identify which transformations are used.

f(x)=x−3+4 
h(x)=x+7−−−−−√ 
g(x)=1x−5 
f(x)=−3x3 
h(x)=(x−7)3+4 
f(x)=14(x−9)2+5 
f(x)=3x+2−−−−−√−6 
f(x)=34(x+5)+45
Answer the following questions:
 What part of the function
g(x)=−(f(x)+1)=−(x3+1) shifts the graph off(x) vertically?  What part of the function
g(x)=−(f(x)+1) reflects the graph off(x) across the xaxis?  What is different between the functions
g(x)=−(x3+1.0) andh(x)=−x3+1.0 that changes the appearance of the graph? 
Write a function
g(x) whose graph looks like the graph off(x)=x reflected across the xaxis and shifted up 1 unit.g(x)= 
How do you transform the graph of:
f(x)=x3 so that it looks like the graph of:f(x)=4x3+6  Stretch it by a factor of ¼ and shift it up 6 units.
 Stretch it by a factor of 6 and shift it left 4 units.
 Stretch it by a factor of 4 and shift it down 6 units.
 Stretch it by a factor of 4 and shift it up 6 units.
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