Question

Assignment: Function Equations Investigation

Answer 1

Function 1:

For the given table

$\begin{array}{cc}x&f(x)\\-2&-2\\-1&1\\0&4\\1&7\end{array}$

you can plot the graph of the function (see first attached diagram). This function is linear and has equation f(x)=3x+4.

Function 2:

For the given function f(x)=-2x+3 you can create a table

$\begin{array}{cc}x&f(x)\\-2&7\\-1&5\\0&3\\1&1\end{array}$

and plot the graph (see second attached diagram).

Function 3:

For the given graph of the function, you can find the function:

$\dfrac{x-0}{6-0}=\dfrac{y-(-3)}{0-(-3)},\\ \\\dfrac{x}{6}=\dfrac{y+3}{3},\\ \\2(y+3)=x,\\ \\y=\dfrac{1}{2}x-3.$

Thus, the equation of the function 3 is $f(x)=\dfrac{1}{2}x-3.$

The table will take a look

$\begin{array}{cc}x&f(x)\\-2&-4\\-1&-3.5\\0&-3\\1&-2.5\end{array}$