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University of California, Berkeley

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Problem 53

Writing In Exercises 53 and $54,$ use a graphing utility to graph each function $f$ in the same viewing window for $c=-2$ , $c=-1, c=1,$ and $c=2 .$ Give a written description of the change in the graph caused by changing $c .$

$$\begin{array}{l}{\text { (a) } f(x)=c \sin x} \\ {\text { (b) } f(x)=\cos (c x)} \\ {\text { (c) } f(x)=\cos (\pi x-c)}\end{array}$$

Answer

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## Discussion

## Video Transcript

Okay, so these are fallen graft part one part a one C is equal to negative too. You'd have won and won. This is our graph for part B, and this is our graph part.

## Recommended Questions

Writing In Exercises 53 and $54,$ use a graphing utility to graph each function $f$ in the same viewing window for $c=-2,$ $c=-1, c=1,$ and $c=2 .$ Give a written description of the change in the graph caused by changing $c .$

$$\begin{array}{l}{\text { (a) } f(x)=\sin x+c} \\ {\text { (b) } f(x)=-\sin (2 \pi x-c)} \\ {\text { (c) } f(x)=c \cos x}\end{array}$$

Identifying Graphs In Exercises 51 and $52,$ the graphs of

$f, f^{\prime},$ and $f^{\prime \prime}$ are shown on the same set of coordinate axes.

Identify each graph. Explain your reasoning. To print an

enlarged copy of the graph, go to MathGraphs.com.

Identifying Graphs In Exercises 51 and $52,$ the graphs of

$f, f^{\prime},$ and $f^{\prime \prime}$ are shown on the same set of coordinate axes.

Identify each graph. Explain your reasoning. To print an

enlarged copy of the graph, go to MathGraphs.com.

In Exercises $51 - 54 ,$ complete parts $( a ) , ($ b) $,$ and $( c )$ for the piecewise-defined function.

(a) Draw the graph of $f .$

(b) Determine $\lim _ { x \rightarrow c ^ { + } } f ( x )$ and $\lim _ { x \rightarrow c ^ { - } } f ( x )$

(c) Writing to Learn Does $\lim _ { x \rightarrow c } f ( x )$ exist? If so, what is it? If not, explain.

$$c = 2 , f ( x ) = \left\{ \begin{array} { l l } { 3 - x , } & { x < 2 } \\ { \frac { x } { 2 } + 1 , } & { x > 2 } \end{array} \right.$$

On the basis of the results of Exercises $52-55,$ describe the transformation that transforms the graph of a function $f(x)$ into the graph of the function $f(c x),$ where $c$ is a constant with $0<$ $c<1 .$ [Hint: How are the two graphs related to the $y$ -axis?]

In Exercises $45-52,$ use the graph of $y=f(x)$ to graph each function $g .$

$$

g(x)=2 f(x-1)

$$

On the basis of the results of Exercises $48-50,$ describe the transformation that transforms the graph of a function $f(x)$ into the graph of the function $f(c x),$ where $c$ is a constant with $c>1 .$ [Hint: How are the two graphs related to the $y$ -axis? Stretch your mind.]

In Exercises $45-52,$ use the graph of $y=f(x)$ to graph each function $g .$

$$

g(x)=\frac{1}{2} f(2 x)

$$

In Exercises $45-52,$ use the graph of $y=f(x)$ to graph each function $g .$

$$

g(x)=2 f\left(\frac{1}{2} x\right)

$$

In Exercises $45-52,$ use the graph of $y=f(x)$ to graph each function $g .$

$$

g(x)=\frac{1}{2} f(x+1)

$$