Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.1 - Functions - Exercises - Page 157: 75


(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.)
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