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Algebra Ch4 Functions Review 4.1-3 New 4.4-6 Write this down: • Function – a relationship between variables in which each value of the input variable is associated with a unique value of the output variable. • Can be shown as graphs, tables, equations, or words, sets of ordered pairs. Linear Functions • Functions that can be defined by linear equations • Linear equations are first-degree equations – no powers of 2 or greater. • Slope-intercept form: y = mx + b • Function notation: f(x) = mx + b • Sample: when m = 2 and b = 3, f(x) = 2x + 3 Sample: when m = 2 and b = 3, f(x) = 2x + 3 f(x) = 2x + 3 (x, f(x)) f(0) = 2(0) + 3 = 0 + 3 = 3 (0, 3) f(1) = 2(1) + 3 = 2 + 3 = 5 (1, 5) For each x value, there is only one f(x) value. Not a function: x = k because there is more than one value. If x = 3, then y can be any + or – value. A vertical line is not a function! • 4.1 We have already used graphs to relate 2 quantities. Page 252/8,9,10 • 4.2 Patterns & Linear Functions. – A dependent variable changes in response to another variable, the independent variable. – Input – independent variable – Output – dependent variable – 257/problem 2. As the number of photos (independent variable) increases, the amount of memory (dependent variable)decreases. 4.3 Patterns & Nonlinear Functions See page 262. • Linear Function – its graph is a nonvertical line or part of a nonvertical line • Nonlinear Function – its graph is not a line or part of a line 4.4: graphing of a function rule Continuous graph – unbroken • Discrete graph – composed of distinct isolated points Page 270. Problem 1 Page 271, problem 2 Page 272, problem 3 Assignment: 274/9-21, 38-54evens Day2, 4.4, page 273, prob. 4 • Graphing nonlinear function rules • A. y = lXl – 4 • B. y = x2 + 1 273, problem 4 #4. • Graph: y = x3 + 1 • Assignment: 275/23-31, 39-53odd Nov. 29 Assignment: 283/8-14,16-18