For the graph of $f$: Find
$y=5$ on the Y axis , then find the point(s) on the graph of
$f$ with second coordinate $5$, determine it's first
coordinate, $\approx \pi/12$, and that is the key desired value for $x$. |
For the mapping diagram of $f$:
Find $y=5$ on the target axis , then find $x$ on the source
axis with the function arrow pointing to $5$. |

To do this, look for the point where the graph of $f$ intersects the line $y=5$. | To do this,look for the arrow that joins the point $x \approx \pi/12$ on the source axis to the point $y=5$ on the target axis. |

Comments: You can move the (red) point labelled x on the left axis of the mapping diagram to a position where the arrow head points to $f(x) = 5$ and the corresponding point on the graph of $f$ will move to the position where the graph of $f$ crosses the line $ y = 5$.

Check the box and the diagram will show the solution on both the mapping diagram and the graph.

You can use the sliders to investigate other examples by $A,B,$ as well as $D$.