Lecture Note Function
Example 4
A manufacturer can produce radios at a cost of $10 apiece an estimated that if they are
sold for x dollars, consumers will buy approximately 80 −xradios each month.
Express the manufacturer’s monthly profit as a function of the price x, graph this
function, and determine the price at which the manufacture’s profit will be greatest.
Solution
Begin by stating the desired relationship in words:
Profit = (number of radios sold) (profit per radio)
Now replace the words by algebraic expressions. You know that :
Number of radios sold = 80 – x
and since the radios are produced at a cost of $10 apiece and sold for x dollars
apiece,
It follows that profit per radio = 80 −x
LetPx() denotes the profit and conclude that
() ( )( )
Px=− −=−+− 80 x x 10 x^290 x 800
3 Linear Functions
Linear function is a function that changes at a constant rate with respect to its
independent variable. The graph of a linear function is a straight line. The equation of
a linear function can be written in the form
ymxb= +
where m and b are constants.
3.1 The Slope of a Line ...................................................................................
The slope of a line is the amount by which the y coordinate of a point on the line
changes when the x coordinate is increased by 1.
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2
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1
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y=x^2 -6x+3- 5 3 + 5(3;-5)XY