Consider the linear function $f(x) = mx + b$. This is studied
extensively with its graph in most texts.
We will examine mapping figures for an alternative
visualization of the key features of $f $.-
You should first review
Example LF.0 to explore for your self how the numbers
$m$ and $b$ are realized in the features of the mapping diagram.
Before further discussion of we'll examine some simple and
Now that you've looked a some simple
examples here are five more [important] examples for the linear
function $f(x) = mx + b$. Each has the same "constant", $1$, so
these examples illustrate the effect of the linear
Here is a link to a spreadsheet for exploring
the effects of $m$ and $b$ on the mapping diagram for a linear
You can use the following dynamic example
to see the effects of the linear coefficient simultaneously on a
mapping diagram and a graph.
Dynamic Visualization for Linear
Functions: Graphs, and Mapping Diagrams
Still to investigate:??
Parallel Lines: m=m'
m*m' = -1
See also previous work by Martin Flashman, Yoon Kim, and Ken
Yanosko, introducing mapping diagrams with dynamics: Visualizing
Functions Pages 2-6