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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 
_________________________________________________________________ 
____________  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 \begin{align*}y = x^{2}\end{align*} , in order to graph \begin{align*}g(x) = 3(x  4)^{2} + 2\end{align*} ?
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: \begin{align*}f(x) = x^2 + 3\end{align*}
 Write a function that will horizontally stretch the following: \begin{align*}f(x) = x^2  6\end{align*}
 Rewrite this function \begin{align*}f(x) = \sqrt{x}\end{align*} to get a reflection over the xaxis.
 Rewrite this function \begin{align*}f(x) = \sqrt{x}\end{align*} to get a reflection over the yaxis.
Graph each of the following using transformations. Identify which transformations are used.
 \begin{align*}f(x) = x3 + 4\end{align*}
 \begin{align*}h(x) = \sqrt{x + 7}\end{align*}
 \begin{align*}g(x) = \frac{1}{x  5}\end{align*}
 \begin{align*}f(x) = 3x^3\end{align*}
 \begin{align*}h(x) = (x  7)^3 + 4\end{align*}
 \begin{align*}f(x) = \frac{1}{4}(x  9)^2 + 5\end{align*}
 \begin{align*}f(x) = 3\sqrt{x + 2}  6\end{align*}
 \begin{align*}f(x) = \frac{3}{4(x + 5)} + \frac{4}{5}\end{align*}
Answer the following questions:
 What part of the function \begin{align*}g(x) = (f(x) + 1) = (x^3 + 1)\end{align*} shifts the graph of \begin{align*}f(x)\end{align*}vertically?
 What part of the function \begin{align*}g(x) = (f(x) + 1)\end{align*} reflects the graph of \begin{align*}f(x)\end{align*} across the xaxis?
 What is different between the functions \begin{align*}g(x) = (x^3 + 1.0)\end{align*} and \begin{align*}h(x) = x^3 + 1.0\end{align*} that changes the appearance of the graph?
 Write a function \begin{align*}g(x)\end{align*} whose graph looks like the graph of \begin{align*}f(x) = x\end{align*} reflected across the xaxis and shifted up 1 unit. \begin{align*}g(x) =\end{align*}

How do you transform the graph of: \begin{align*}f(x) = x^3\end{align*} so that it looks like the graph of:\begin{align*}f(x) = 4x^3 + 6\end{align*}
 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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