Functions & Their Graphs (P3) September 10th, 2012.

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Functions & Their Graphs (P3) September 10th, 2012

I. Functions & Function Notation Ex. 1: For the function f defined by f(x) = 3x 2 - 4x, evaluate each expression. a. f(-1) b. f(3a) c. f(b+2) d.

You try: For the function f defined by f(x)=2x+4, evaluate

The Domain & Range of a Function Def. The domain is the set of all input values for x. The range is the set of all outcomes of f(x).

Ex. 2: Find the domain and range of each function. a. f(x)=x 2 +2 b. c. h(t)=sec t d.

III. The Graph of a Function Def: An equation represents a function if for each x- value, there only exists one corresponding y-value, or it passes the vertical line test. Ex. 3: Determine whether y is a function of x. a. b.b.

IV. Transformations of Functions Basic Transformations (c>0): Original Graph y=f(x) Horizontal shift c units right y=f(x-c) Horizontal shift c units left y=f(x+c) Vertical shift c units up y=f(x)+c Vertical shift c units down y=f(x)-c Reflection about the x-axis y=-f(x) Reflection about the y-axis y=f(-x) Reflection about the origin y=-f(-x)

Ex. 4: Describe each transformation, then use your description to write an equation for each graph. a.

b.

c.

d.

e.

V. Classifications & Combinations of Functions Def: The composite of function f with function g is given by The domain of f(g(x)) is the set of all x in the domain of g such that g(x) is in the domain of f. Ex. 5: Given and, find each composite function. a. b.

You Try: Given and, find each composite function. a. b. c.

Def: A function y=f(x) is even if f(-x)=f(x). It is odd if f(- x)=-f(x). Even functions are symmetric about the y-axis, odd functions are symmetric about the origin. Ex. 6: Determine whether each function is even, odd, or neither. Then use a graphing utility to verify your result. a. b. c.