Precalc0105to0107-page13

Precalc0105to0107-pa - algebra course but linear combinations of functions will enable us to take a broader view of symmetry in Section 1.7 • We

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(Section 1.6: Combining Functions) 1.6.1 SECTION 1.6: COMBINING FUNCTIONS LEARNING OBJECTIVES • Know how to add, subtract, multiply, and divide functions. • Be able to identify linear combinations of functions. • Know how to construct and decompose composite functions. • Find the domains of the functions that result from these operations. • Be able to model functions using constraint equations and composite functions. PART A: DISCUSSION • In Section 1.5, we constructed functions from pieces of functions on disjoint (non-overlapping) subdomains. • In this section, we will combine functions by adding , subtracting , multiplying , and dividing them over basically the same domain. • Linear combinations are usually not formally introduced to students until a linear
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Unformatted text preview: algebra course, but linear combinations of functions will enable us to take a broader view of symmetry in Section 1.7. • We will also combine functions by composing them. This corresponds to the successive application of functions. We did this when we transformed functions and graphs in Section 1.4. • Calculus theorems , including linearity theorems and the Chain Rule for differentiating composite functions, will use the notation and ideas of this section. Composite functions are also related to the u-substitution technique of integration. • In applied calculus problems such as related rates and optimization problems, we will need to devise functions, compose them, and combine them with constraint equations ....
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This document was uploaded on 12/29/2011.

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