standard_description: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
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