Discussion:  All Topics in PreCalculus for Properties of Rational Functions 
Topic:  Need some quick help 
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Subject:  RE: Need some quick help 
Author:  ycc 
Date:  Aug 3 2004 
> 1. Suppose you have a lemonade stand, and when you charge $1 per cup of
> lemonade you sell 60 cups. But when you raise your price to $2 you only
sell
> 30 cups. Write an equation for the number of cups you sell as a function
of
> the price you charge. Denote "C" for number of cups, and "P" for the
price
> you charge. Assume the function is linear.
>
>
>
Since the function is linear, therefore we may assume C=aP+b where a, b are
constants to be determined.
Now you know, when C=60, P=1. So, we have 60=a*1+b
Similarly when C=30, P=2, so 30=a*2+b
We have two equations with two variables. Solve for a and b will give you
the
answers.
> 2. Take a look at the table below and write out an equation for f(x).
>
> x 2 1 0 1 2
> f(x) 5 2 1 4 7
>
>
Suppose the function is linear. Let f(x)=ax+b.
Same as Q.1, put x=0, f(x)=1, we have 1=a*0+b, hence b=1.
put x=2, f(x)=7, then 7=a*2+1, hence.....
Check all points with the formula!
 
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