Basics of functions and their graphs - презентация, доклад, проект скачать

Нажмите для полного просмотра!

Basics of functions and their graphs, слайд №1

Basics of functions and their graphs, слайд №2

Basics of functions and their graphs, слайд №3

Basics of functions and their graphs, слайд №4

Basics of functions and their graphs, слайд №5

Basics of functions and their graphs, слайд №6

Basics of functions and their graphs, слайд №7

Basics of functions and their graphs, слайд №8

Basics of functions and their graphs, слайд №9

Basics of functions and their graphs, слайд №10

Basics of functions and their graphs, слайд №11

Basics of functions and their graphs, слайд №12

Basics of functions and their graphs, слайд №13

Basics of functions and their graphs, слайд №14

Basics of functions and their graphs, слайд №15

Basics of functions and their graphs, слайд №16

Basics of functions and their graphs, слайд №17

Basics of functions and their graphs, слайд №18

Basics of functions and their graphs, слайд №19

Basics of functions and their graphs, слайд №20

Basics of functions and their graphs, слайд №21

Содержание ▲

Вы можете ознакомиться и скачать презентацию на тему Basics of functions and their graphs. Доклад-сообщение содержит 21 слайдов. Презентации для любого класса можно скачать бесплатно. Если материал и наш сайт презентаций Mypresentation Вам понравились – поделитесь им с друзьями с помощью социальных кнопок и добавьте в закладки в своем браузере.

Слайды и текст этой презентации

Слайд 1

Описание слайда:

Слайд 2

Описание слайда:

Objectives: Find the domain and range of a relation. Determine whether a relation is a function. Determine whether an equation represents a function. Evaluate a function. Graph functions by plotting points. Use the vertical line test to identify functions. Obtain information about a function from its graph. Identify the domain and range of a function from its graph. Identify intercepts from a function’s graph.

Слайд 3

Описание слайда:

Definition of a Relation A relation is any set of ordered pairs. The set of all first components of the ordered pairs is called the domain of the relation and the set of all second components is called the range of the relation.

Слайд 4

Описание слайда:

Example: Finding the Domain and Range of a Relation Find the domain and range of the relation: {(0, 9.1), (10, 6.7), (20, 10.7), (30, 13.2), (40, 21.2)} domain: {0, 10, 20, 30, 40} range: {9.1, 6.7, 10.7, 13.2, 21.2}

Слайд 5

Описание слайда:

Definition of a Function A function is a correspondence from a first set, called the domain, to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range.

Слайд 6

Описание слайда:

Example: Determining Whether a Relation is a Function Determine whether the relation is a function: {(1, 2), (3, 4), (6, 5), (8, 5)} No two ordered pairs in the given relation have the same first component and different second components. Thus, the relation is a function.

Слайд 7

Описание слайда:

Functions as Equations If an equation is solved for y and more than one value of y can be obtained for a given x, then the equation does not define y as a function of x.

Слайд 8

Описание слайда:

Example: Determining Whether an Equation Represents a Function Determine whether the equation defines y as a function of x. The shows that for certain values of x, there are two values of y. For this reason, the equation does not define y as a function of x.

Слайд 9

Описание слайда:

Function Notation The special notation f(x), read “f of x” or “f at x”, represents the value of the function at the number x.

Слайд 10

Описание слайда:

Example: Evaluating a Function If evaluate Thus,

Слайд 11

Описание слайда:

Graphs of Functions The graph of a function is the graph of its ordered pairs.

Слайд 12

Описание слайда:

Example: Graphing Functions Graph the functions f(x) = 2x and g(x) = 2x – 3 in the same rectangular coordinate system. Select integers for x, starting with –2 and ending with 2.

Слайд 13

Описание слайда:

Example: Graphing Functions (continued) We set up a partial table of coordinates for each function.

Слайд 14

Описание слайда:

The Vertical Line Test for Functions If any vertical line intersects a graph in more than one point, the graph does not define y as a function of x.

Слайд 15

Описание слайда:

Example: Using the Vertical Line Test Use the vertical line test to identify graphs in which y is a function of x.

Слайд 16

Описание слайда:

Example: Analyzing the Graph of a Function Use the graph to find f(5)

Слайд 17

Описание слайда:

Identifying Domain and Range from a Function’s Graph To find the domain of a function from it’s graph, look for all the inputs on the x-axis that correspond to points on the graph. To find the range of a function from it’s graph, look for all the outputs on the y-axis that correspond to points on the graph.

Слайд 18

Описание слайда:

Example: Identifying the Domain and Range of a Function from Its Graph Use the graph of the function to identify its domain and its range. Domain Range

Слайд 19

Описание слайда:

Example: Identifying the Domain and Range of a Function from Its Graph Use the graph of the function to identify its domain and its range. Domain Range

Слайд 20

Описание слайда:

Identifying Intercepts from a Function’s Graph To find the x-intercepts, look for the points at which the graph crosses the x-axis. To find the y-intercept, look for the point at which the graph crosses the y-axis. A function can have more than one x-intercept but at most one y-intercept.