Answer
(a)
$T(x)=0.08x$
(b)
$\begin{array}{ccc}
\\\text{Purchase Amount, }(x) &\text{Tax, }T(x)
\\0 &0
\\100 &8
\\200 &16
\\300 &24
\\400 &32
\end{array}$
(c)
Refer to the attached image below for the graph.
Work Step by Step
(a) Algebraic Representation
The tax, $T(x)$, is $8\%$ of the purchase price (x).
Thus, the algebraic representation of the function is:
$T(x)=8\%(x)
\\T(x) = 0.08x$
(b) Numerical Representation
Create a table of values where $x$ and $T(x)$ are both in dollars, to have:
$\begin{array}{ccc}
\\\text{Purchase Amount, }(x) &\text{Tax, }T(x)
\\0 &0
\\100 &8
\\200 &16
\\300 &24
\\400 &32
\end{array}$
(c) Graphical Representation
Plot each ordered pair in the table of part (b), then connect the points using a line. (Refer to the attached image below for the graph.)
