Exercises LF.0

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.
Download worksheet for this section: Worksheet.LF.pdf.

For each linear function complete the function table and then create the corresponding mapping diagram and locate the "focus point" (possibly infinite).

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

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

$x$	$f(x)= -x + 1$
2
1
0
-1
-2

$x$	$f(x)= x+1$
2
1
0
-1
-2

For each linear function complete the function table and then create the corresponding mapping diagram and locate the focus point.

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

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

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

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

For the linear functions in problem 1 c and 1 d, use the focus point to find $f(0)$ and the value of $a$ where $f(a) = 0$.
For the linear functions in problem 2 c and 2 d, use the focus point to find $f(0)$ and the value of $a$ where $f(a) = 0$.
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 $f$.
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. $f(x)=-\frac 1 2 x + \frac 1 2$
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. $f(x)=-\frac 1 2 x + \frac 1 2$