Increasing and Decreasing Functions Lesson 5 1 The

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Increasing and Decreasing Functions Lesson 5. 1

Increasing and Decreasing Functions Lesson 5. 1

The Ups and Downs � Think of a function as a roller coaster going

The Ups and Downs � Think of a function as a roller coaster going from left to right � Uphill ◦ Slope > 0 ◦ Increasing function � Downhill ◦ Slope < 0 ◦ Decreasing function 2

Definitions � Given function f defined on an interval ◦ For any two numbers

Definitions � Given function f defined on an interval ◦ For any two numbers x 1 and x 2 on the interval � Increasing function ◦ f(x 1) < f(x 2) when x 1 < x 2 � Decreasing function ◦ f(x 1) > f(x 2) when x 1< x 2 X 1 X 2 f(x) 3

Domain: In a set of ordered pairs, (x, y), the domain is the set

Domain: In a set of ordered pairs, (x, y), the domain is the set of all x -coordinates. Range: In a set of ordered pairs, (x, y), the range is the set of all ycoordinates.

The set of ordered pairs may be a limited number of points. Given the

The set of ordered pairs may be a limited number of points. Given the following set of ordered pairs, find the domain and range. Ex: {(2, 3), (-1, 0), (2, -5), (0, -3)} Domain: Range: {2, -1, 0} {3, 0, -5, -3} If a number occurs more than once, you do not need to list it more than one time.

The set of ordered pairs may be an infinite number of points, described by

The set of ordered pairs may be an infinite number of points, described by a graph. Given the following graph, find the domain and range.

Domain: {all real numbers} Range: {y: y≥ 0}

Domain: {all real numbers} Range: {y: y≥ 0}

The set of ordered pairs may be an infinite number of points, described by

The set of ordered pairs may be an infinite number of points, described by an algebraic expression. Given the following function, find the domain and range. Example: Domain: Range: {x: x≥ 5} {y: y≥ 0}

2. Domain={x: x } Range: {all reals}

2. Domain={x: x } Range: {all reals}