Click on this link for a file that has Mapping Diagram blanks (2 and 3 axes) for use in the following exercises.
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.  $f(x)=-\frac 1 2 x + \frac 1 2$