Intermediate Algebra, Chapter 3, 3.6, Section 3.6, Problem 38

a.) Solve the equation $x - 4y = 8$ for $y$ in terms of $x$, and rewrite the equation using function notation $f(x)$.


$
\begin{equation}
\begin{aligned}

x - 4y =& 8
&& \text{Given equation}
\\
\\
-4y =& -x + 8
&& \text{Subtract each side by $x$}
\\
\\
y =& \frac{1}{4}x - \frac{8}{4}
&& \text{Divide each side by $-4$}
\\
\\
y =& \frac{1}{4}x - 2


\end{aligned}
\end{equation}
$


So,

$\displaystyle f(x) = \frac{1}{4} x - 2 \qquad y = f(x)$

b.) Find $f(3)$.


$
\begin{equation}
\begin{aligned}

f(3) =& \frac{1}{4} (3) - 2
\qquad \text{Let } x = 3
\\
\\
=& \frac{3}{4} - 2
\\
\\
=& - \frac{5}{4}

\end{aligned}
\end{equation}
$