• I can add, subtract, multiply and divide functions. • I can compose functions. • I can use the composition of functions in real world situations.

Lesson 4.6 ~ Function operations OBJECTIVES:

PLEASE NOTE: The notation for the composition of two functions is sometimes confused with the notation for the product of two functions (parentheses often mean multiplication). There are definite differences however.

• While multiplication of functions is commutative (it can be done in any order), the composition of functions is not. Order matters. • The product of two functions involves multiplying each term of one function by each term of the other (distribution). The composition of two functions involves REPLACING the variable of the first function with the expression given by the other function.

In Method 1, we compose the two functions first, then substitute -3 in for x in the composition.

In Method 2, we evaluate the second function at -3, then substitute that value in for x in the first function.

Homework:

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