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 Discussion: All Topics Topic: Need some quick help

 Post a new topic to the General Discussion in PreCalculus for Properties of Rational Functions discussion

 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

> 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!