Questions: f(x)=A sec B x The graph has the shape of the secant stretched vertically by a factor of 3 . Thus, A=3. f(x)=3 sec B x The graph begins at x=0 and ends at x=π/2. Thus, the period is π/2-0 =π/2. The period is given by 2π/B, thus we have 2π/B =π/2 2π =π/2 B B =2π/1 * 2/π=4 Thus, A=3, B=4. Therefore, f(x)= 3 sec 4 x
Transcript text: \[
f(x)=A \sec B x
\]
The graph has the shape of the secant stretched vertically by a factor of 3 .
Thus, $A=3$.
\[
f(x)=3 \sec B x
\]
The graph begins at $x=0$ and ends at $x=\frac{\pi}{2}$.
Thus, the period is $\left.\frac{\pi}{2}-0 \right\rvert\,=\frac{\pi}{2}$.
The period is given by $\frac{2 \pi}{B}$, thus we have
\[
\begin{aligned}
\frac{2 \pi}{B} & =\frac{\pi}{2} \\
2 \pi & =\frac{\pi}{2} B \\
B & =\frac{2 \pi}{1} \cdot \frac{2}{\pi}=4
\end{aligned}
\]
Thus, $A=3, B=4$.
Therefore, $f(x)=$ $\square$ $\square \mathrm{sec}$
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