Podcast
Questions and Answers
Qual data corresponde al die de le section 1.3?
Qual data corresponde al die de le section 1.3?
9/6
Que lection esseva planificate pro le 9 de septembre 2024?
Que lection esseva planificate pro le 9 de septembre 2024?
Section 1.4
Que leccion esseva realizate inter le 11 e le 12 de septembre?
Que leccion esseva realizate inter le 11 e le 12 de septembre?
Section 1.5b - 1.6
Qual documentos esseva incluse in le lection de 1.5a?
Qual documentos esseva incluse in le lection de 1.5a?
Signup and view all the answers
In que die esseva lection 1.4 presentate?
In que die esseva lection 1.4 presentate?
Signup and view all the answers
Que numero de pagina esseva le ultime pagina in le lection 1.5b?
Que numero de pagina esseva le ultime pagina in le lection 1.5b?
Signup and view all the answers
Que hora esseva quando le lection 1.5a esseva realisate?
Que hora esseva quando le lection 1.5a esseva realisate?
Signup and view all the answers
Qual es le prime pagina de lection 1.4?
Qual es le prime pagina de lection 1.4?
Signup and view all the answers
Flashcards
Section
Section
Le section de un libro o documento, usualmente marcate con un numero o littera.
Quick Notes Page
Quick Notes Page
Le pagina in un libro o documento que contine notas e informationes importante.
Taking Notes
Taking Notes
Le processo de organisation e summarisation del material in un curso.
Lesson Sequence
Lesson Sequence
Signup and view all the flashcards
Lesson
Lesson
Signup and view all the flashcards
Block Day
Block Day
Signup and view all the flashcards
Course Structure
Course Structure
Signup and view all the flashcards
Course Content
Course Content
Signup and view all the flashcards
Study Notes
Early Bird Question
- A question posed at the start of a class session.
- Example given: "What is your favorite subject in school?"
Learning Targets
-
Students are given learning objectives for a particular lesson.
-
Example: "I will use slope to graph linear equations in two variables".
Linear Equations
-
Includes various forms of linear equations.
-
General form: Ax + By + C = 0
-
Vertical line: x = a
-
Horizontal line: y = b
-
Slope-intercept form: y = mx + b
-
Point-slope form: y - y₁ = m(x - x₁)
-
Two-point form: .
Using Slope
- Discussion points about slope.
- What is slope?
- What kinds of things have slope?
- Slope-intercept form of an equation: y = mx + b, where m is the slope and b is the y-intercept.
Finding Slope
- Calculate slope from two points (x₁, y₁) and (x₂, y₂).
- The formula: m = (y₂ - y₁)/(x₂ - x₁).
Finding the Slope (multiple points)
- Calculation of slope using specific points, with instructions to maintain consistency in the order of subtraction.
Writing Linear Equations
- Describing the point-slope form as a helpful method for finding equations of lines.
Parallel and Perpendicular Lines
- Definition of parallel lines (equal slopes).
- Definition of perpendicular lines (negative reciprocal slopes).
- How slope relates to parallel and perpendicular lines.
Application
-
Discussion on how slope is used in real situations.
-
Explaining the difference between slope as a ratio and a rate.
Application Examples
- Slope used in ramp steepness.
- Linear sales for a company over time
- Discussing the slope as a ratio or a rate in real-world situations
Summary of Equations of a Line
- General form: Ax + By + C = 0
- Vertical line: x = a
- Horizontal line: y = b
- Slope-intercept form: y = mx + b
- Point-slope form: y - y₁ = m(x - x₁)
- Two-point form: (y-y₁)/(x-x₁) = (y₂-y₁)/(x₂-x₁)
Function and Function Notation
-
Relation: A rule of correspondence that relates two variables.
-
Function: A special relation that matches each item from one set with exactly one item from a different set.
-
Definition of Function: A definition of Function (relation, assigns to each element of set A, exactly one element of set B. The set A, is the domain, the set B contains the range.)
Function and Function Notation - Discrete
- Representing functions in discrete mathematics.
Function and Function Notation - Continuous
- Representing functions using equations and formulas in algebra.
Function and Function Notation - Examples
-
Examples comparing relations and functions.
-
(1,9), (2,13), (3, 15), (4,15), (5,12), (6,10)
-
Graphs showing increasing, decreasing, and constant behavior.
Graphing Functions or relations
-
Four ways of representing a function.
-
Verbally by an equation describing relationship of input/output variables.
-
Numerically with table/list of ordered pairs.
-
Graphically as points on coordinates.
-
Algebraically by an equasion with 2 variables.
Function and Function Notation - Input/output/relationship/equation examples
- Graph of function values(input/output).
Function and Function Notation - Discrete vs Continuous
Function and Function Notation - Name each part
- y= dependent variable
- x= independent variable
- Relationship of inputs and outputs (domain and range)
Function and Function Notation - Determining if an equation represents a function of x
Function and Function Notation - Input / Output/ equation example
- Example of input/output (f(x)).
Piecewise-Defined Function
- Definition of Piecewise function
- Example of a piecewise function.
Finding Zeros
- Zeros of a function f, these are the x values for which f(x) = 0
- x-intercept of the graph of the function
Finding Intercepts
- Calculate x-intercepts (x_0) or y-intercepts (y_0).
Domain
-
Definition of the domain of a function ( all real numbers for which an expression is defined).
-
Implied domain examples ( avoid even roots of negative numbers in functions).
-
Examples of functions with given domains.
Difference Quotient
- one of the basic definitions in calculus employing the ratio (f(x + h) - f(x)) / h
Difference Quotient, Examples (Function)
- Calculation of the difference quotient for given functions.
Application – Volume of a can
- Calculating the volume of the can as a function of radius.
- Calculating the volume as a function of height.
Summary
- Summary of Key ideas (bullet-point list)
Homework
- Homework assigned (assignment details).
Early Bird Question (example)
- Question posed at the start of the lesson
- Example given: "What is your favorite sport to play?"
Homework
- Instructions for turning in homework via the Teams assignment system.
Quick Check
- Quick check for the lesson (instructions and examples).
Learning Targets (example)
- I will find zeros of functions.
- I will identify even and odd functions.
- I will apply the Greatest Integer Function.
Increasing and Decreasing
- Definitions of increasing, decreasing and constant behaviour of a function.
Average Rate of Change
- Finding the average rate of change for a function (given input and output values and specific points).
Even and Odd Functions
-
Identifying even and odd functions.
-
Determining whether a function qualifies as even or odd.
Calculators
- Using calculators for tasks.
- Specific tasks like graphing, finding zeros, relative minimums and maximums.
Library of Parent Functions
- The parent functions (various mathematical relationships).
Step Functions (Greatest Integer Function)
- Definition of Greatest Integer function.
- Examples of Greatest Integer function.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Este quiz aborda a compreensão e a aplicação de equações lineares, incluindo a forma de interseção de slope e a forma ponto-slope. Os estudantes aprenderão a calcular o slope entre dois pontos e aplicar diferentes formas de equações lineares. Ideal para aqueles que desejam melhorar suas habilidades matemáticas.
