Click on this link for a file that has Mapping Diagram blanks (2 and 3 axes) for use in the following exercises.
You may want to try this using a spreadsheet. You can download a spreadsheet template for linear functions by clicking here.
1. For each  linear function complete the function table and then create the corresponding mapping diagram and locate the "focus point" (possibly infinite).

a.
 $x$ $f(x)=2x$ 2 1 0 -1 -2

b.
 $x$ $f(x)= -2x$ 2 1 0 -1 -2

c.
 $x$ $f(x)= -x + 1$ 2 1 0 -1 -2
d.
 $x$ $f(x)= x+1$ 2 1 0 -1 -2
2. For each  linear function complete the function table and then create the corresponding mapping diagram and locate the focus point.

a.
 $x$ $f(x)=\frac 1 2 x$ 2 1 0 -1 -2

b.
 $x$ $f(x)=-\frac 1 2 x$ 2 1 0 -1 -2

c.
 $x$ $f(x)=\frac 1 2 x + \frac 1 2$ 2 1 0 -1 -2
d.
 $x$ $f(x)=-\frac 1 2 x + \frac 1 2$ 2 1 0 -1 -2
3. For the linear functions in problem 1 and 1 d, use the focus point to find $f(0)$ and the value of $a$ where $f(a) = 0$.
4. For the linear functions in problem 2 and 2 d, use the focus point to find $f(0)$ and the value of $a$ where $f(a) = 0$.
5. Suppose $f$ is a linear function with $f(1)= 3$ and $f(3) = 1$.
a. Find the focus point of $f$ on a mapping diagram.
b. Use the focus point to find $f(0)$.
c. Determine $m$, the magnification factor of $f$.
d. Give two point slope forms for $f$ based on the given information and the slope intercept form for $f$.
6. For each  linear function  create a mapping diagram for the function treated as a composition of core linear functions.
a. $f(x)=2x + 1$                        b. $f(x)= -2x - 3$
c. $f(x)=\frac 1 2 x + \frac 1 2$            d.  $f(x)=-\frac 1 2 x + \frac 1 2$
7.  For each  linear function  use "socks and shoes" to find and create a mapping diagram for the function for its inverse linear function.
a. $f(x)=2x + 1$                        b. $f(x)= -2x - 3$
c. $f(x)=\frac 1 2 x + \frac 1 2$            d.  $f(x)=-\frac 1 2 x + \frac 1 2$