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
important examples.

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 coefficient, $m$

Here is a link to a spreadsheet for exploring the effects of $m$ and $b$ on the mapping diagram for a linear function.

You can use the following dynamic example to see the effects of the linear coefficient simultaneously on a mapping diagram and a graph. Still to investigate:??

Parallel Lines: m=m'

Perpendicular Lines

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