Answer
See below:
Work Step by Step
Consider the provided function,
$ y=\frac{1}{2}\sec 2\pi x $
By use the reciprocal function,
$ y=\frac{1}{2}\cos 2\pi x $
Now substitute different values of $ x $ in the provided function to find the values of $ y $. As the interval is given, put values of $ x $ in the range of the interval, $\text{0}\le x\le 2$
To find the key points of the function, put $ x=0$ in the provided function,
$\begin{align}
& y=\frac{1}{2}\cos 2\pi x \\
& =\frac{1}{2}\cos \left( 2\pi \cdot 0 \right) \\
& =\frac{1}{2}\cdot 1 \\
& =\frac{1}{2}
\end{align}$
And, put $ x=\frac{1}{4}$
$\begin{align}
& y=\frac{1}{2}\cos 2\pi x \\
& =\frac{1}{2}\cos \left( 2\pi \cdot \frac{1}{4} \right) \\
& =\frac{1}{2}\cdot 0 \\
& =0
\end{align}$
And, put $ x=\frac{1}{2}$
$\begin{align}
& y=\frac{1}{2}\cos 2\pi x \\
& =\frac{1}{2}\cos \left( 2\pi \cdot \frac{1}{2} \right) \\
& =\frac{1}{2}\cdot \left( -1 \right) \\
& =-\frac{1}{2}
\end{align}$
And, put $ x=\frac{3}{4}$
$\begin{align}
& y=\frac{1}{2}\cos 2\pi x \\
& =\frac{1}{2}\cos \left( 2\pi \cdot \frac{3}{4} \right) \\
& =\frac{1}{2}\cdot 0 \\
& =0
\end{align}$
And, put $ x=1$
$\begin{align}
& y=\frac{1}{2}\cos 2\pi x \\
& =\frac{1}{2}\cos \left( 2\pi \cdot 1 \right) \\
& =\frac{1}{2}\cdot 1 \\
& =\frac{1}{2}
\end{align}$
And, put $ x=\frac{5}{4}$
$\begin{align}
& y=\frac{1}{2}\cos 2\pi x \\
& =\frac{1}{2}\cos \left( 2\pi \cdot \frac{5}{4} \right) \\
& =\frac{1}{2}\cdot \left( 0 \right) \\
& =0
\end{align}$
And, put $ x=\frac{3}{2}$
$\begin{align}
& y=\frac{1}{2}\cos 2\pi x \\
& =\frac{1}{2}\cos \left( 2\pi \cdot \frac{3}{2} \right) \\
& =\frac{1}{2}\cdot \left( -1 \right) \\
& =-\frac{1}{2}
\end{align}$
And, put $ x=\frac{7}{4}$
$\begin{align}
& y=\frac{1}{2}\cos 2\pi x \\
& =\frac{1}{2}\cos \left( 2\pi \cdot \frac{7}{4} \right) \\
& =\frac{1}{2}\cdot \left( 0 \right) \\
& =0
\end{align}$
And, put $ x=2$
$\begin{align}
& y=\frac{1}{2}\cos 2\pi x \\
& =\frac{1}{2}\cos \left( 2\pi \cdot 2 \right) \\
& =\frac{1}{2}\cdot \left( 1 \right) \\
& =\frac{1}{2}
\end{align}$
