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Teacher: Nguyen Thi Le Nhung
Exponential Functions.
1. Functions.
2. Composition of functions.
DUY TAN UNIVERSITY
Section 1: Functions.
1. Exponential Functions.
If b is a positive number other than 1 (b > 0, b  1 ) ,
there is a unique function called the exponential funtcion
with base b that is defined by
f ( x)  b x for every real number x
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Section 1: Functions.
Figure 1 Typical exponential graphs
Section 1: Functions.
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Example 1: Give f ( x) 
4  x2
a) Find the domain of function.
b) Compute f (1), f (2), f (3) .
Solution
a) The function is defined when 4  x  0  x  4
2
2
 2  x  2
The domain of f is the set of all real numbers in D   2,2
b) f (1)  4  12  3, f (2)  0
Since x  3  D  f (3) is undefined .
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Section 1: Functions.
Example 2.
Suppose the total cost in dollars of manufacturing q units of a certain
commodity is given by the function
C (q)  q 3  30q 2  500q  200
a) Compute the cost of manufacturing 10 units of the commodity.
b) Compute the cost of manufacturing the 10th unit of the commodity.
Solution
a) Cost of 10 units = C (10)  103  30(10)2  500(10)  200
 3200 dollars
b) Cost of the 10th unit  C (10)  C (9)
 3200  2999  201 dollars
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Section 1 : Functions.
Example 3.
Suppose that t hours past midnight, the temperature in Miami was
1 2
C (t )  t  4t  10 degrees Celsius
6
a) What was the temperature at 2:00 P.M.?
b) By how much did the temperature increase or decrease between
6:00 and 9:00P.M.?
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Section 1: Functions.
Example 4.
An efficiency study of the morning shift at a certain factory indicates
that an average worker who arrives on the job at 8:00 A.M. will have
assembled
3
2
f ( x)   x  6 x  15 x
television sets x hours later.
a) How many sets will such a worker have assembled by 10:00 A.M ?
b) How many sets will such a worker assemble between 9:00 and
10:00 A.M.?
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Thank you for listening!