🗊Презентация Functions and their graphs

Категория: Математика
Нажмите для полного просмотра!
Functions and their graphs, слайд №1Functions and their graphs, слайд №2Functions and their graphs, слайд №3Functions and their graphs, слайд №4Functions and their graphs, слайд №5Functions and their graphs, слайд №6Functions and their graphs, слайд №7Functions and their graphs, слайд №8Functions and their graphs, слайд №9Functions and their graphs, слайд №10Functions and their graphs, слайд №11Functions and their graphs, слайд №12Functions and their graphs, слайд №13Functions and their graphs, слайд №14Functions and their graphs, слайд №15Functions and their graphs, слайд №16Functions and their graphs, слайд №17Functions and their graphs, слайд №18Functions and their graphs, слайд №19Functions and their graphs, слайд №20Functions and their graphs, слайд №21Functions and their graphs, слайд №22Functions and their graphs, слайд №23Functions and their graphs, слайд №24
Скачать
Вы можете ознакомиться и скачать презентацию на тему Functions and their graphs. Доклад-сообщение содержит 24 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


Functions and Their Graphs 1.2 – Functions
Описание слайда:
Functions and Their Graphs 1.2 – Functions

Слайд 2


Vocab Function = A set of ordered pairs that has each input (x) giving exactly one output (y) Ex: Function or not? In a function, one input can’t give 2 different outputs!
Описание слайда:
Vocab Function = A set of ordered pairs that has each input (x) giving exactly one output (y) Ex: Function or not? In a function, one input can’t give 2 different outputs!

Слайд 3


More Vocab (x, y) = (input, output) f(x) is another way to write an output Domain = the set of all inputs (x) Range = the set of all outputs (y) Ex: For the function f(x) = x – 3 , evaluate the following: f(-3) f(x+1)
Описание слайда:
More Vocab (x, y) = (input, output) f(x) is another way to write an output Domain = the set of all inputs (x) Range = the set of all outputs (y) Ex: For the function f(x) = x – 3 , evaluate the following: f(-3) f(x+1)

Слайд 4


Ex: For the function f(x) = 2 – x2 , evaluate the following: Ex: For the function f(x) = 2 – x2 , evaluate the following: f(x+1) Ex: For the function f(x) = x2 + x , evaluate the following: f(2x)
Описание слайда:
Ex: For the function f(x) = 2 – x2 , evaluate the following: Ex: For the function f(x) = 2 – x2 , evaluate the following: f(x+1) Ex: For the function f(x) = x2 + x , evaluate the following: f(2x)

Слайд 5


Ex: For the function f(x) = x2 – 2x + 3, evaluate the following: Ex: For the function f(x) = x2 – 2x + 3, evaluate the following: f(x+h)
Описание слайда:
Ex: For the function f(x) = x2 – 2x + 3, evaluate the following: Ex: For the function f(x) = x2 – 2x + 3, evaluate the following: f(x+h)

Слайд 6


Ex: For the function f(x) = 2x2 – 3 , evaluate the following: Ex: For the function f(x) = 2x2 – 3 , evaluate the following: The difference quotient
Описание слайда:
Ex: For the function f(x) = 2x2 – 3 , evaluate the following: Ex: For the function f(x) = 2x2 – 3 , evaluate the following: The difference quotient

Слайд 7


f(x) = 5x + 6. Find f(x – 3). 5x – 3 5x + 3 5x – 9 5x – 15
Описание слайда:
f(x) = 5x + 6. Find f(x – 3). 5x – 3 5x + 3 5x – 9 5x – 15

Слайд 8


f(x) = 2x – x2 . Find f(x + 1). -x2 + 1 -x2 + 2x + 1 -x2 +4x + 3 -x2
Описание слайда:
f(x) = 2x – x2 . Find f(x + 1). -x2 + 1 -x2 + 2x + 1 -x2 +4x + 3 -x2

Слайд 9


Ex: The function below is a piecewise function. Find f(0) and f(1). Ex: The function below is a piecewise function. Find f(0) and f(1). Since 0<1, use the top function for f(0). f(0) = -3! Since 1≥1, use the bottom function for f(1). f(1) = -2!
Описание слайда:
Ex: The function below is a piecewise function. Find f(0) and f(1). Ex: The function below is a piecewise function. Find f(0) and f(1). Since 0<1, use the top function for f(0). f(0) = -3! Since 1≥1, use the bottom function for f(1). f(1) = -2!

Слайд 10


More Vocab y = x2 means y is a function of x Y is not a function of x when a ± is in play Ex: Which of these has y as a function of x? x2 – y = 7 Solve for y first… - y = 7 – x2 y = x2 – 7 … no ± means YES! x2 + y2 = 2x y2 = 2x – x2 y = … so NO!
Описание слайда:
More Vocab y = x2 means y is a function of x Y is not a function of x when a ± is in play Ex: Which of these has y as a function of x? x2 – y = 7 Solve for y first… - y = 7 – x2 y = x2 – 7 … no ± means YES! x2 + y2 = 2x y2 = 2x – x2 y = … so NO!

Слайд 11


Finding Domain and Range The domain (set of all x’s) is always assumed to be all real numbers unless some values cannot create outputs (y’s). Ex: Find the domain of the following functions: y = 2x – 3 Any x will produce a y, so the domain is xϵℝ (all reals) y = The square root can’t be negative, so the domain is x≥0 y = The denominator can’t be 0, so 2x – 4 ≠0… …x≠2
Описание слайда:
Finding Domain and Range The domain (set of all x’s) is always assumed to be all real numbers unless some values cannot create outputs (y’s). Ex: Find the domain of the following functions: y = 2x – 3 Any x will produce a y, so the domain is xϵℝ (all reals) y = The square root can’t be negative, so the domain is x≥0 y = The denominator can’t be 0, so 2x – 4 ≠0… …x≠2

Слайд 12


Finding Domain and Range To find range, graph the function and infer the range (set of all y’s). Ex: Find the domain and range of the function Graph the function first. For the domain, we know from the equation given that x ≥ 3. Our graph confirms that. For the range, the graph shows us that there are no negative values for y, and the values will continue to increase as x increases. Range: y ≥ 0
Описание слайда:
Finding Domain and Range To find range, graph the function and infer the range (set of all y’s). Ex: Find the domain and range of the function Graph the function first. For the domain, we know from the equation given that x ≥ 3. Our graph confirms that. For the range, the graph shows us that there are no negative values for y, and the values will continue to increase as x increases. Range: y ≥ 0

Слайд 13


What is the domain? xϵℝ -2≤x≤2 x≥0 -2<x<2
Описание слайда:
What is the domain? xϵℝ -2≤x≤2 x≥0 -2<x<2

Слайд 14


What is the domain? xϵℝ x ≠ -2 x ≠ 3 x ≠ -2 and x ≠ 3
Описание слайда:
What is the domain? xϵℝ x ≠ -2 x ≠ 3 x ≠ -2 and x ≠ 3

Слайд 15


What is the range? yϵℝ y ≠ 5 y < -5 y ≥ -5
Описание слайда:
What is the range? yϵℝ y ≠ 5 y < -5 y ≥ -5

Слайд 16


Ch. 1 – Functions and Their Graphs 1.3 – More Functions
Описание слайда:
Ch. 1 – Functions and Their Graphs 1.3 – More Functions

Слайд 17


Vertical Line Test Vertical is up and down! Vertical Line Test: If you can draw some vertical line on a graph and it goes through MORE THAN ONE point, the graph is NOT a function. Ex: Are these graphs functions?
Описание слайда:
Vertical Line Test Vertical is up and down! Vertical Line Test: If you can draw some vertical line on a graph and it goes through MORE THAN ONE point, the graph is NOT a function. Ex: Are these graphs functions?

Слайд 18


Vocab As we read left to right, the function to the right is… …decreasing in the red region Decreasing for x<-1, so we write to indicate that y decreases over that x interval …constant in the blue region Constant for -1≤x≤2, so we write …increasing in the green region Increasing for x>2, so we write
Описание слайда:
Vocab As we read left to right, the function to the right is… …decreasing in the red region Decreasing for x<-1, so we write to indicate that y decreases over that x interval …constant in the blue region Constant for -1≤x≤2, so we write …increasing in the green region Increasing for x>2, so we write

Слайд 19


Vocab When a function goes from increasing to decreasing (or visa versa), it will have a relative minimum or a relative maximum. The graph below has a relative maximum at (-2, 2) and a relative minimum at (1, -2). A graph can have any amount of relative minima or maxima.
Описание слайда:
Vocab When a function goes from increasing to decreasing (or visa versa), it will have a relative minimum or a relative maximum. The graph below has a relative maximum at (-2, 2) and a relative minimum at (1, -2). A graph can have any amount of relative minima or maxima.

Слайд 20


Functions A function is even if it is symmetric about the y-axis f(-x) = f(x) A function is odd if it is symmetric about the origin f(-x) = -f(x) A graph symmetric about the x-axis is… …not a function!
Описание слайда:
Functions A function is even if it is symmetric about the y-axis f(-x) = f(x) A function is odd if it is symmetric about the origin f(-x) = -f(x) A graph symmetric about the x-axis is… …not a function!

Слайд 21


The function y = 4x2 – 2 is… Even Odd None of the above Not a function
Описание слайда:
The function y = 4x2 – 2 is… Even Odd None of the above Not a function

Слайд 22


The function y = 1/x is… Even Odd None of the above Not a function
Описание слайда:
The function y = 1/x is… Even Odd None of the above Not a function

Слайд 23


The function y = x3 – x is… Even Odd None of the above Not a function
Описание слайда:
The function y = x3 – x is… Even Odd None of the above Not a function

Слайд 24


Functions and their graphs, слайд №24
Описание слайда:

Скачать

Похожие презентации
Mypresentation.ru
Загрузить презентацию