Beginning Algebra With Applications, Chapter 5, 5.5, Section 5.5, Problem 34

Determine the range of the function given by the equation $\displaystyle f(x) = \frac{3}{4}x-1$ if the domain is $\{ -8,-4,0,4,8 \}$.


$
\begin{equation}
\begin{aligned}

f(-8) =& \frac{3}{4} (-8)-1
\qquad \text{Replace $x$ by each member of the domain}
\\
=& -6-1
\\
=& -7
\\
f(-4) =& \frac{3}{4} (-4)-1
\\
=& -3-1
\\
=& -4
\\
f(0) =& \frac{3}{4} (0)-1
\\
=& 0-1
\\
=& -1
\\
f(4) =& \frac{3}{4} (4)-1
\\
=& 3-1
\\
=& 2
\\
f(8) =& \frac{3}{4} (8)-1
\\
=& 6-1
\\
=& 5

\end{aligned}
\end{equation}
$


The range is $\{ -7,-4,-1,2,5 \}$.

The ordered pairs $(-8,-7), (-4,-4), (0,-1), (4,2)$ and $(8,5)$ belong to the function.