Chapter 2: Analysis of Graphs of Functions

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Presentation transcript:

Chapter 2: Analysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs 2.4 Absolute Value Functions 2.5 Piecewise-Defined Functions 2.6 Operations and Composition

Operations and Composition Operations on Functions Given two functions f and g, then for all values of x for which both f(x) and g(x) are defined, the functions f + g, f − g, fg, and f/g are defined as follows.

Examples Using Operations on Functions Let f(x) = x2 + 1 and g(x) = 3x + 5. Perform the operations. a. (f + g)(1) b. (f − g)(−3) c. (fg)(5) d. (f/g)(0)

Examples Using Operations on Functions

Evaluating Combinations of Functions If possible, use the given graph of f and g to evaluate (a) (f − g)(−2) (b) (f · g)(1) (c) (f / g)(0)

The Difference Quotient

Finding the Difference Quotient Let f(x) = 2x2 − 3x. Find the difference quotient and simplify.

Finding the Difference Quotient Let f(x) = 2x2 − 3x. Find the difference quotient and simplify.

Composition of Functions If f and g are functions, then the composite function, or composition, of g and f is

Evaluating Composite Functions

Finding Composite Functions Solution

Decomposing Composite Functions