Math Is Fun Forum

Tim Aschauer

Guest

Function rules and how to create them

I need to create function rules for the following:

the change from a $10 bill when you buy hamburgers for $1.50 each=

The number of peices of candy you have if each house gives you 5 and you eat 4 on the way home=

The amount of money you earn at $6 per hour=

Any help would be appreciated, thank you

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Function rules and how to create them

Each function has an input (that you can change) and an output (that changes depending on what your input is).

One way of working out what a function should be is to work out the output when you put the input as 0 and 1. I'll do the first one to show you what I mean.

First let's see what happens when you buy no hamburgers. You spend no money, and so your change from £10 is ... £10. Obvious, but still a useful statement.

Now we'll buy a burger. That cost £1.50, and so your change from £10 is £8.50.

Combining those results shows that buying one more hamburger gets you £1.50 less change.
Therefore, the formula (where C is change and H is hamburgers) is C = 10 - 1.5H.

In general, if f(0) is the output of a function when you input 0, and f(1) is the output when you input 1, then the formula for the function is f(0) + [f(1)-f(0)]x, where x is the input.

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Why did the vector cross the road?
It wanted to be normal.