Aclub is planning on printing custom t-shirts for the 2013 academic year.
- the company fittees' set-up fee is $50
- the first 50 shirts are priced at $7.99 each
- any additional shirts are priced at $6.99 each
how much does it cost to order 40 shirts? 80 shirts?
find piecewise defined formula for the total cost of ordering x shirts and simplify.

Set up fee is always there so there is always 50 starting feee

first 50 shirts means   every shirt up to and including the 50th shirt cost 7.99 each

any number past that (51st shirt and beyond) is 6.99

40 shirts
this is 50 and below and also add set up fee
50+40*7.99=$369.60

$369.60 for 40 shirts

80 shirts
this is above 50, BUT, the first 50 are still 7.99 each, the rest are 6.99
80-50=30
don't forgeet set up fee
so
50+50*7.99+30*6.99=659.20
cost for 80 shirts is $659.20

piecewise function
y=mx+b form is nice
first part is easy (x≤50 part)
y=7.99x+50

for the bit that is over the 50, we have to include the 50 shirts in the b
50*7.99=399.50
and the setup is 50 so add that also
399.50+50=449.50
and subtract the 50 from x
y=6.99(x-50)+449.50

therefor the piecewise functin is