1.4 Linear Functions and Models

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1.4 Linear Functions and Models

• Rita Korsunsky

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1.4 Linear Functions and Models




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Example slope, zero, x and y- intercepts
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Example slope, zero, x and y- intercepts
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Example Discrete Function
The junior class has paid 100 to a disc jockey
for a dance. Tickets for the dance are 4 each.
Express the net income as a function of the
number of tickets sold. Identify the point where
the class makes a profit.
n lt 25 class loses money n 25 class breaks
even n gt 25 class makes profit
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Example Step Graph

• The phone company charges 20 cents the first
  minute for a long distance call and 10 cents for
  each additional minute rounded to the next
  minute. Graph the function of the cost of a call
  lasting t minutes.

Time in min t Cost in cents C(t)





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Example Break-Even Point
A recording studio invests 24,000 to produce a
master tape of a singing group. It costs 1.50 to
make each copy of the master and cover the
operating costs.
a) Express the cost of producing t tapes as a
function C(t).
b) If each tape is sold for 6.50, express the
revenue (the total amount received from the sale)
as a function R(t).
c) Sketch the graphs of the functions C and R.
d) Find the coordinates of the break-even point
(that is, where the graphs intersect).