standard_description: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
problem_activity: Task
The table below shows some input-output pairs of two functions $f$ and $g$ that agree for the values that are given but some of their output values are missing.
|  $t$   |   |   |   |   |   |   |   |   |
|--------|---|---|---|---|---|---|---|---|
| $f(t)$ |   |   |   |   |   |   |   |   |
| $g(t)$ |   |   |   |   |   |   |   |   |
Complete the table in a way so that $f$ could be invertible and so that $g$ is definitely not invertible.
Graph both functions and explain from the graph why $f$ is invertible and $g$ is not.
Come up with two real life situations that $f$ and $g$ could be representing.
Find and interpret the value $f^{-1}(4)$ in terms of these contexts.


aligns: no