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Composition of Functions
Composition of the function f with the function g, given by , is defined by:
Domain of consists of all x in domain of g such that is in the domain of f.
Example. :If and , find:
Example: Use the graphs of f and g to evaluate each expression.
Example: In the example above, for what value (s) of x is ?
Horizontal Compression and Elongation of Graphs . If
a) For any constant , the graph of is the same as that of with a
change in the horizontal scale.
1) If horizontal compression
2) If horizontal elongation
b) The graph of is a reflection about the y-axis of the graph of .
1) For horizontal compression and reflection.
2) For horizontal elongation and reflection.
Example: Graph the following functions:
Example: If , , and , find:
Example: Use the graph of the function given below to
sketch the graph of the indicated
Example: Write the function
as the composition of three functions.
Applied Example: The number of bacteria in a refrigerated food is given by
where t is the Celsius temperature of the food. when
the food is removed from refrigeration , the temperature is given by
where t is the time in hours.
a) What does the composite function represent?
b) How many bacteria are in the food when t=2 hours?