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10.2 Product and Quotients of Functions
f ( x) and g ( x)
•
•
•
•
are functions that exist and are defined over a domain.
 f  g  ( x)  f ( x)  g ( x)
Sum
Difference  f  g  ( x)  f ( x)  g ( x)
 f  g  ( x )  f ( x ) g ( x )
Product
Quotient  f 
f ( x)
, g ( x)  0
  ( x) 
g ( x)
g
Why are there restrictions on the variable or non‐permissible values for a variable?
Math 30‐1
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The product of two linear functions is a quadratic function.
The quotient of two linear functions is a rational function.
Determine the product of the functions in simplest form. f ( x)   x  3
2
h( x)  fg ( x)
 f ( x) g ( x)
  x  3  x  2 
2
g ( x)  x  2
h( x )   x 2  6 x  9   x  2 
h( x)  x3  4 x 2  3 x  18
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Determine the quotient of the functions in simplest form. r ( x)  x  1
s ( x)  x 4  2 x3  5 x 2  7 x  5
s
h( x )    ( x )
r
s ( x)
h( x ) 
r ( x)
x 4  2 x3  5 x 2  7 x  5
h( x ) 
x 1
h( x)  x 3  3 x 2  2 x  5, x  1
Math 30‐1
Sketch the graph of h(x) = fg(x)
Domain
Range
3
Sketch the graph of h(x) = (ff)(x)
What would the graph of
h(x) = (f/f)(x) look like?
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g
f 
  x  Sketch the graph of h( x)   g   x 
 
 f 
Sketch the graph of h( x)  
Domain
Range
 x | x  3
 y | y  7
Domain
 x | x  2
Range
1

y | y   
2

Math 30‐1
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Consider the function h(x) to be in the form h( x)  f  g ( x)  k ( x)
h( )  sin 2   sin   cos 
Determine the expressions for f(x), g(x), and k(x)
h( )  sin   sin   1  cos 
f ( )  sin 
g ( )  sin   1
k ( )  cos 
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