What does "interpret the point" mean?

Question

As far as I understand, interpreting a function means finding its vertex, determining its shape and the direction, in which the function's hands are pointing. For example, if I am asked to interpret the following function: $y\ =\ 4\left(x-3\right)^{2}+2$, then I would say that this is a parabola, its hands are pointing upward and its vertex is located at the point (4,2).

However, here I have a task, in which I am asked to "find and interpret" a point of a function:

I don't quite understand what I am asked to do here.

Answer 1

Typically in situations like this, "find and interpret a value" or "find and interpret a point" means to perform any calculations necessarily, and then tell how the result refers back to the story. (This is more a conceit of educational pedagogy than mathematics terminology.)

In this case, interpreting $f(60)$ might look something like: "At $t=60$, $f(t)=50$, suggesting that after 60 minutes, we will have traveled 50 miles." Your results may vary depending on whether there is any additional story nearby in the text.

Answer 2

The question is not entirely clear on details but it seems $f(t)$ indicates either distance (from some reference point) of an object in miles at time $t$ in minutes.

So $f(60)$ likely indicates distance travelled by the object at $60$ minutes, or $1$ hour.

And $f^{-1}$ refers to the inverse function so it accepts as an argument the distance and returns the time. So $f^{-1}(60)$ should indicate the time taken to have travelled $60$ miles.

It is possible the question was referring to displacement rather than distance, but without further details, it is impossible to be sure.