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: 73

Answer

(a) Algebraic representation: $f(x)=\dfrac{x}{3} + \dfrac{2}{3}$, which can also be written as $f(x)=\dfrac{x+2}{3}$ (b) Numerical representation: $\begin{array}{ccc} x & f(x) \\-8 &2 \\-5 &1 \\-2 &0 \\1 &1 \\4 &2 \\\end{array}$ (c) Refer to the attached image below for the graphical representation of the function.
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Work Step by Step

(a) Divide the input by 3 means $\dfrac{x}{3}$. Thus, the algebraic representation of the function is: $f(x) = \dfrac{x}{3}+\dfrac{2}{3} \\f(x)=\dfrac{x+2}{3}$ (b) To represent the function numerically, create a table of values to have: $\begin{array}{ccc} \\x & f(x) \\-8 &2 \\-5 &1 \\-2 &0 \\1 &1 \\4 &2 \\\end{array}$ (c) To represent the function graphically, 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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