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**Section 8.1 #13** Plot $f(x)=4\cos \left(\pi x\right)$.

*Solution*: There is a vertical stretch of $4$ and a horizontal compression by $\pi$ (meaning we divide anchor points by $\pi$):

**Section 8.1 #18** Plot $f(t)=2\sin \left( t - \dfrac{5\pi}{6} \right)$.

*Solution*: There is a vertical stretch by $2$ and a horizontal shift right by $\dfrac{5\pi}{6}$:

**Section 8.1 #19** Plot $f(t)=-\cos \left( t + \dfrac{\pi}{3} \right)+1$.

*Solution*: There is a vertical reflection, a horizontal shift left by $\dfrac{\pi}{3}$, and a vertical shift up by $1$:

**Section 8.2 #24** Plot $f(x)=4\tan(x)$.

*Solution*: There is a vertical stretch of $4$:

**Section 8.2 #31** Plot $f(x)=7\sec(5x)$.

*Solution*: There is a vertical stretch by $7$ and a horizontal compression by $5$ (meaning we divide $x$-values by $5$):

**Section 8.2 #32** Plot $f(x)=\dfrac{9}{10} \csc(\pi x)$.

*Solution*: There is a vertical compression by $\dfrac{9}{10}$ and a horizontal compression by $\pi$ (meaning we divide $x$-values by $\pi$):