0. Functions

How do you obtain the graph of $y=f\left(3x\right)$ from the graph of $y=f\left(x\right)$?

Use the graph of $f$ in the figure to plot the following functions.

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$y=f\left(x-2\right)$

Use the graph of $f$ in the figure to plot the following functions.

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$y=f\left(x-1\right)+2$

Shifting a graph Use a shift to explain how the graph of $\text{ƒ}\left(x\right)=\sqrt{-x^2+8x+9}$ is obtained from the graph of $g\left(x\right)=\sqrt{25-x^2}$ . Sketch a graph of ƒ.

Use shifts and scalings to transform the graph of $\text{ƒ}\left(x\right)=x^2$ into the graph of g. Use a graphing utility to check your work.

$g\left(x\right)=\text{ƒ}(2x-4)$

Use shifts and scalings to transform the graph of $\text{ƒ}\left(x\right)=x^2$ into the graph of g. Use a graphing utility to check your work.

$g\left(x\right)=6\text{ƒ}\left(\frac{x-2}{3}\right)+1$

Use shifts and scalings to transform the graph of $\text{ƒ}\left(x\right)=\sqrt{x}$  into the graph of g. Use a graphing utility to check your work.

$g\left(x\right)=2\text{ƒ}(2x-1)$

Use shifts and scalings to transform the graph of $\text{ƒ}\left(x\right)=\sqrt{x}$  into the graph of g. Use a graphing utility to check your work.

$g\left(x\right)=3\sqrt{x-1}-5$

Use shifts and scalings to graph the given functions. Then check your work with a graphing utility. Be sure to identify an original function on which the shifts and scalings are performed.

$g\left(x\right)=-3x^2$

Use shifts and scalings to graph the given functions. Then check your work with a graphing utility. Be sure to identify an original function on which the shifts and scalings are performed.

$h\left(x\right)=-4x^{{}^2}-4x+12$

The graph of ƒ is shown in the figure. Graph the following functions. <IMAGE>

a. $\text{ƒ}(x+1)$

The graph of ƒ is shown in the figure. Graph the following functions. <IMAGE>

$f\left(2\right(x-1\left)\right)$

Shifting and Scaling Graphs

Suppose the graph of g is given. Write equations for the graphs that are obtained from the graph of g by shifting, scaling, or reflecting, as indicated.

f. Compress horizontally by a factor of 5

Describe how each graph is obtained from the graph of 𝔂 = ƒ(x).

a. 𝔂 = ƒ(x - 5)

Describe how each graph is obtained from the graph of 𝔂 = ƒ(x).

d. 𝔂 = ƒ(2x + 1)