College Algebra, Chapter 3, 3.1, Section 3.1, Problem 68

A verbal description of a function "Let $V(d)$ be the volume of a sphere of diameter $d$. To find the volume, take the cube of the diameter, then multiply by $\pi$ and divide by 6." Find (a) Algebraic, (b) Numerical, and (c) Graphical presentations for the functions.

a.) Algebraically (using a formula)
The description tell us that take the cube of the diameter $d$, then multiply by $\pi$ and divide by 6. So we get $\displaystyle V(d) = \frac{d^3 \pi}{6}$.

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

$
\begin{array}{|c|c|}
\hline\\
x & V(d)\\
\hline\\
-2 & - \frac{4}{3} \pi\\
\\
-1& - \frac{1}{6} \pi\\
\\
0 & - 0\\
\\
1 & \frac{1}{6} \pi\\
\\
2 & \frac{4}{3} \pi\\
\\
\hline
\end{array}
$


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