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.
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)
