Increasing and Decreasing Functions Lesson 5 1 The
- Slides: 10
Increasing and Decreasing Functions Lesson 5. 1
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 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 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 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 a graph. Given the following graph, find the domain and range.
Domain: {all real numbers} Range: {y: y≥ 0}
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}
- Lesson 4 increasing and decreasing functions
- First derivative increasing decreasing
- Aims and objectives of increasing and decreasing functions
- Strictly increasing and decreasing functions
- Increasing decreasing constant functions
- Piecewise function increasing decreasing
- Decreasing intension
- How to find increasing and decreasing intervals on a graph
- Removable and non removable discontinuities
- Increasing intervals
- Increasing and decreasing recipes