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.