Example 1. $ f(x) = 2x + 1; g(x) = 3x + 2$.
Dynamic Views for Composition of Linear Functions $f \circ
g$:Tables and Mapping Diagrams
$f(x)= m_fx + b_f$ and $g(x) = m_gx+b$
$(f \circ g)(x) = f(g(x)) =f(3x+2)= 2*(3x+2) + 1 = (6x +4) +1=
6x + 5$
- Click on the arrow button in the figure to start the
- The button will change to a "pause" button, which can be used
to halt the animation.
Notice how the point on the graph is paired with the points and
arrow on the mapping diagram.
- Check the box to see the mapping diagram and graph of $f$ .
- Check the box to see the mapping diagram and graph of $f \circ
- Select the point $x$ in the mapping diagram to move the point
by mouse or use the scroll up or down key to move by
increments of 1.
INsert GeoGebra Here;
|For the graph of $f$: Find
$y=20$ on the Y axis , then find the point on the graph of
$f$ with second coordinate $20$, determine it's first
coordinate, $6$, and that is the desired value for $x$.
||For the mapping diagram of $f$:
Find $y=20$ on the target axis , then find $x$ on the source
axis with the function arrow pointing to $20$.
|To do this, look for the point where the line
$y=20$ intersects the line that is the graph of $f$
||To do this, find the focus point of
$f$, $F= [5, -10]$ on the mapping diagram. [Use Geogebra?]
Draw the line through F and the point $y=20$, to find the
point of intersection of this line with the X axis, $x=6$,
which is the desired value for $x$.