Chapter 2 - Section 2.1 - Functions - Exercises - Page 157: 74

(a) $f(x)=\frac{3}{4}(x-4)$ (b) $\begin{array}{ccc} \\x &f(x) \\-4 &-6 \\0 &-3 \\4 &0 \\8 &3 \end{array}$ (c) Refer to the attached image below for the graph.

Work Step by Step

(a) Algebraic Representation Subtract 4 from the input, where the input is $x$, means $x-4$. Thus, the algebraic representation of the function is: $f(x)=\frac{3}{4}(x-4)$ (b) Numerical Representation Create a table of values to have: $\begin{array}{ccc} \\-4 &-6 \\0 &-3 \\4 &0 \\8 &3 \end{array}$ (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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