standard_description: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
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