The Algebra of Functions continued

by Amy Benson

The Functions

In this investigation we will look at f(x) = 5x+2 and g(x) = -6x+4.

So, when h(x) represents the sum of f(x) and g(x),

h(x) = -x+6

For h(x), the product of f(x) and g(x)

 

The quotient is

 

Finally, the composite of f(x) and g(x) is

h(x) = -30x + 22

Examining the mulitple functions h(x) leads to the discovery that the product and the composite have the same leading coeffient. This is true for all linear functions f(x) and g(x).


The Graphs

f(x), g(x) and h(x) where h(x) is the sum of f(x) and g(x)

 

f(x), g(x) and h(x) where h(x) is the product of f(x) and g(x)

 

f(x), g(x) and h(x) where h(x) is the quotient of f(x) and g(x)

f(x), g(x) and h(x) where h(x) is the composite of f(x) and g(x)

 


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