For the graph of $f$ and $g$: Find the point at the intersection of the graphs of $f$ and $g$, $(x_*,y_*)$, determine it's first coordinate, $x_*$, and that is the desired value for $x$, and its second coordinate, $y_*$, is the desired value for $y$.

For the mapping diagram of $f$ and $g$: Find the focus points of $f$, $F= [m_f, b_f]$, and $g$, $G=[m_gb_g]$, on the mapping diagram. Draw the line through $F$ and $G$, to find the point of intersection of this line with the X axis, $x=x_*$, which is the desired value for $x$ and the Y axis, $y=y_*$ for the desired value of $y$. Notice how the point on the graph is paired with the points and arrow on the mapping diagram.

• Enter expressions in the input boxes to change the functions $f$ or $g$.
• Check the box to see the focus points (when $m \ne 1$) and lines from the point $x=0$ on the mapping diagram.
  
• Check the box to see the solution of the equation visualized on the graph and the mapping diagram.

Martin Flashman, Aug. 11, 2018, Created with GeoGebra