Use the graph of $f$ in the figure to plot the following functions.
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$y=f\left(x-2\right)$

Given the equation $y=f(x-3)+2$, what kind of transformation does this represent?

How do you obtain the graph of $y=f\left(x+2\right)$ from the graph of $y=f\left(x\right)$?

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

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

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.

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