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:

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

  • 1
    $\begingroup$ "interpret" just has the usual English meaning, it is only related to the direction of the "function's hands" in the particular quadratic example you gave. In this case it might mean something like f(60) = distance in miles traveled after 60 min. $\endgroup$
    – YiFan Tey
    Nov 3, 2021 at 6:13

2 Answers 2


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.


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.


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