Explain why each function is continuous or discontinuous.
(a) The temperature at a specific location as a function of
(b) The temperature at a specific time as a function of the dis-
tance due west from New York City
(c) The altitude above sea level as a function of the distance
due west from New York City
(d) The cost of a taxi ride as a function of the distance traveled
(e) The current in the circuit for the lights in a room as a function of time
I just don't know where to begin with this question.
I would begin by understanding the meaning of a continuous function versus a discontinuous function.
Originally Posted by bhaktir
I do not think that this exercise has anything to do with limits, but reviewing the concept of continuity certainly comes right before an introduction to limits.
They just want you to consider the given functions. Is the function value changing smoothly, as the input increases (or changes)? If it is, then the function is continuous. If the function value jumps from one number to another, without taking on every value inbetween, then the behavior is not smooth, and the function is discontinuous.
Simply explain, in each scenario, why the function changes continuously versus discontinuously.
Have you ever watched the meter in a taxi, as the fare increases? I mean, if you're not familiar with how taxi fares are calculated, then you might not get this one. Let us know.
Part (e) is vague. Some rooms have lights that NEVER turn off, but I'm sure that they are referring to a common room, like the bathroom or bedroom in your apartment.
Cheers ~ Mark
EDIT: Somebody pointed out to me that part (e) is not talking about how the function changes when you throw the switch, but, rather, the fact that the power source is alternating current. This is a reasonable assumption because not many structures are supplied with DC power.
Last edited by mmm4444bot; 08-14-2011 at 12:22 AM.
Reason: Purple text, and an italicization (as long as I'm here)
Thanks for the replies! I get it now.