Question

Complete the function table. Than write a rule for the function. Show all your work.

Answer 1

Only two points are given. An infinite number of functions can be written that will have graphs going through those two points. We have to assume the only one you're interested in is the linear function.

You can use the 2-point form of the equation for a line to find the function, then use that to fill in the table.
$y=\left(\dfrac{y_{2}-y_{1}}{x_{2}-x{1}}\right)(x-x_{1})+y_{1}\\\\y=\left(\dfrac{-1-(-4)}{1-(-2)}\right)(x-(-2))-4\\\\y=\dfrac{3}{3}(x+2)-4\\\\y=x-2$

Using this rule Output = Input -2, we can fill in the function table.
$\left\, \begin{array}{cc}-3 & -5\\-2 & -4\\-1 & -3\\0 & -2\\1 & -1 \end{array} \right\,$