Chapter 6: PROPERTIES AND ATTRIBUTES OF FUNCTIONS

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Chapter 6: PROPERTIES AND ATTRIBUTES OF FUNCTIONS by Mind Map: Chapter 6: PROPERTIES AND ATTRIBUTES OF FUNCTIONS

1. Multiple Representation of Functions

1.1. Table

1.1.1. Table of Values x Process y -2 3(-2) + 3 -3 -1 3(-1) + 3 0 0 3(0) + 3 3 1 3(1) + 3 6 2 3(2) + 3 9 Mapping Diagram -2 -3 -1 0 0 3 1 6 2 9 Set of Ordered Pairs (-2, 3), (-1, 0), (0, 3), (1, 6), (2, 9)

1.2. Equation

1.2.1. 2x^2-5x-6

1.3. Graph

1.3.1. Example

1.4. Verbal Description

1.4.1. uses nonvisual language to convey the visual world. It can navigate a visitor through a museum, orient a listener to a work of art, or provide access to the visual aspects of a performance.

1.4.2. Click here

1.5. Overview

2. Comparing Functions

2.1. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=2ahUKEwiLnab-iJngAhUH2qwKHQ8iD6kQwqsBMAB6BAgFEAQ&url=https%3A%2F%2Fwww.khanacademy.org%2Fmath%2Falgebra%2Flinear-word-problems%2Fcomparing-linear-functions%2Fv%2Fcomparing-features-of-functions-1&usg=AOvVaw2IHLNkJU_fy5ro3aM6clcF

2.2. Linear Functions

2.2.1. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=video&cd=2&ved=0ahUKEwitv6SBjZngAhWIVN8KHW5WArwQtwIILjAB&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DAqIMrHOBM4g&usg=AOvVaw0KBg8hDyZBKr_5aKeuJKLl

2.2.2. Example

2.3. Quadratic Functions

2.3.1. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=2ahUKEwjt_J-OjZngAhXFx4MKHVwUBLAQwqsBMAB6BAgAEAQ&url=https%3A%2F%2Fwww.khanacademy.org%2Fmath%2Falgebra%2Fquadratics%2Ffeatures-of-quadratic-functions%2Fv%2Ffinding-features-of-quadratic-functions&usg=AOvVaw2b4bJndQcx58ANAMQx69jJ

2.3.2. Example

3. Piecewise Function

3.1. A piecewise-defined function is one which is defined not by a single equation, but by two or more.

3.1.1. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=2ahUKEwib4biijZngAhVhw4MKHUlIAxQQwqsBMAB6BAgCEAQ&url=https%3A%2F%2Fwww.khanacademy.org%2Fmath%2Falgebra%2Fabsolute-value-equations-functions%2Fpiecewise-functions%2Fv%2Fpiecewise-function-example&usg=AOvVaw1rCwHbQB_yBtrGYxjAzTaI

3.2. Example

4. Operations with Functions

4.1. Operations on functions are similar to operations on numbers. Each operation has a formal definition which produces a new function

4.1.1. Let f(x) = x + 3 and g(x) = x - 2 1) The sum = (f + g)(x) = f(x) + g(x) = x + 3 + x - 2 = 2x + 1 2) The difference = (f - g)(x) = f(x) - g(x) = (x + 3) - (x - 2) = 5 3) The product = (f . g)(x) = f(x) . g(x) = (x + 3)(x - 2) = x2 + x - 6 4) The quotient = (f/g)(x) = f(x)/g(x) = (x + 3)/(x - 2), x does not = 2

4.1.1.1. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=video&cd=2&ved=0ahUKEwj8prTyjpngAhUGVN8KHT3zA6oQuAIIMjAB&url=https%3A%2F%2Fwww.khanacademy.org%2Fmath%2Falgebra2%2Fmanipulating-functions%2Fcombining-functions%2Fv%2Fsum-of-functions&usg=AOvVaw24hf9Nxm8bS_tmr-JecsPk

4.2. Examples

5. Transforming Functions

5.1. In mathematics, particularly in semigroup theory, a transformation is a function f that maps a set X to itself, i.e. f : X → X In other areas of mathematics, a transformation may simply be any function, regardless of domain and codomain.[4] This wider sense shall not be considered in this article; refer instead to the article on function for that sense.

5.1.1. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=video&cd=1&ved=0ahUKEwi1_6SljpngAhXITd8KHfsuBV0QtwIIJzAA&url=https%3A%2F%2Fwww.khanacademy.org%2Fmath%2Falgebra2%2Fmanipulating-functions%2Fstretching-functions%2Fv%2Fshifting-and-reflecting-functions&usg=AOvVaw0e9BGqrvfo_eiSgaJvG8g8

5.2. Example

6. Functions and their Inverse

6.1. An example of an action and its inverse that you might experience in your everyday life is when you put on your shoes in the morning and then take them off at night. Untying your shoe is the inverse of tying your shoe

6.1.1. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=video&cd=1&ved=0ahUKEwj139Ssj5ngAhVqdt8KHUdiAmQQuAIILDAA&url=https%3A%2F%2Fwww.khanacademy.org%2Fmath%2Falgebra2%2Fmanipulating-functions%2Fintroduction-to-inverses-of-functions%2Fv%2Fintroduction-to-function-inverses&usg=AOvVaw2dvdUMpRP-4e4o_599e0XH

6.2. Example

7. Modeling Real World Data

7.1. Modeling Real World Data

7.1.1. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=2ahUKEwj3m-fCj5ngAhUp0YMKHelUDnoQwqsBMAJ6BAgAEAo&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DOY8hPSps808&usg=AOvVaw3XjWRaPy7CDydtlbdU7_GR