When do we apply functions in our daily life? When do we use discrete functions and when do we use continuous function? Any links, perhaps? Thank you.
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2Does your phone display names of people in the address book when they call? – dtldarek Aug 03 '16 at 14:52
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Think of literally anything that happens or could happen. There will be some way of framing it as a function – Owain West Aug 03 '16 at 14:56
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I suspect that one of the most widely used applications for functions at the present time is in working with Microsoft Excel Worksheets. – Dave L. Renfro Aug 03 '16 at 15:58
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Think of any process where an input produces an output; that process is a function. Here's a few examples.
Ever done income taxes? Each tax table inputs your income and outputs your tax, and that's a function. If your income is not listed in the table then there is an explicit continuous formula for that function that you can use instead (the formula is also piecewise linear; the slopes of the pieces depend on your income bracket, higher brackets having higher slopes). If your income tax computation is automated by some software application, the application uses the same function.
Ever laid linoleum tile on a rectangular floor? The number of linoleum tiles you will need is a discrete function of the length and width of your floor.
Ever gone scuba diving? The water pressure is a continuous function of the depth. Knowledge of this function is essential to not dying when you go scuba diving, and computation of this function is pounded into you when you take a scuba diving course.
Ever fired an explosive shell out of a cannon? The angle at which you tilt the cannon is a continuous function of the distance from the cannon to the point where you want the shell to hit the ground. This function is a basic part of military training.
Ever played craps at a casino? Each roll of the pair of dice produces a number from $2$ to $12$, and the probabilities of these rolls are a discrete function expressed as fractions with denominator $36$: the probability of rolling $2$ is $1/36$; the probability of rolling $3$ is $2/36$; ...; the probability of rolling $7$ is $6/36$; ... If you want to maximize your winnings, intimate knowledge of this function is a must.
I could go on, and on, and on, and on...
Lee Mosher
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The definition of a function will not have much application in your daily life. Unless you are, for example, a mathematician or a programmer.
Functions, continuous functions, discrete functions, etc. are fundamental concepts in mathematics. In itself they are too general to have much value, but they are very useful for organizing things that we want to study in mathematics and elsewhere.
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