College Algebra, Chapter 3, 3.1, Section 3.1, Problem 66

A verbal description of a function "To evaluate $g(x)$, subtract 4 from the input and multiply the result by $\displaystyle \frac{3}{4}$." Find (a) Algebraic, (b) Numerical, and (c) Graphical presentations for the functions.

a.) Algebraically (using a formula)
The description tells us that we subtract first the input $x$ by 4 then multiply the result by $\displaystyle \frac{3}{4}$. So we get
$\displaystyle g(x) = \frac{3}{4} (x -4)$

b.) Numberically (using table of values)
Using the algebraic formula of $g(x)$ to construct values of $x$

$
\begin{array}{|c|c|}
\hline\\
x & g(x)\\
\hline\\
-2 & - \frac{9}{2}\\
\\
-1& - \frac{15}{4}\\
\\
0 & - 3\\
\\
1 & - \frac{9}{4}\\
\\
2 & - \frac{3}{2}\\
\\
\hline
\end{array}
$


c.) Graphically (using a graph)
Using the table of values to draw the graph of $g(x)$