Functions algebra 2 ppt

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Unit: Functions

Algebra 1. Not feeling ready for this? Check out Get ready for Algebra 1. Skill Summary Legend Opens a modal. Evaluating functions. What is a function? Opens a modal. Worked example: Evaluating functions from equation Opens a modal. Worked example: Evaluating functions from graph Opens a modal. Evaluating discrete functions Opens a modal. Worked example: evaluating expressions with function notation Opens a modal.

Algebra 2 Lesson Archives

Evaluate functions Get 3 of 4 questions to level up! Evaluate functions from their graph Get 3 of 4 questions to level up!

Evaluate function expressions Get 3 of 4 questions to level up! Inputs and outputs of a function. Worked example: matching an input to a function's output equation Opens a modal. Worked example: matching an input to a function's output graph Opens a modal.

Worked example: two inputs with the same output graph Opens a modal. Quiz 1. Functions and equations. Equations vs.

Obtaining a function from an equation Opens a modal. Function rules from equations Get 3 of 4 questions to level up! Interpreting function notation. Function notation word problem: bank Opens a modal. Function notation word problem: beach Opens a modal. Function notation word problems Get 3 of 4 questions to level up!

Introduction to the domain and range of a function.Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising.

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Algebra 2 Section 10-1 Exponential Functions PowerPoint

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You can change your ad preferences anytime. PPt on Functions. Upcoming SlideShare. Like this presentation? Why not share! Embed Size px. Start on. Show related SlideShares at end. WordPress Shortcode. Published in: TechnologyBusiness.You are now deeper in your Algebra journey and you've just been introduced to this term called a "function". What in the world is a function? Although it may seem at first like a function is some foreign creature in Algebra land, a function is really just an equation with a fancy name and fancy notation.

If you are nervous, Algebra Class offers many lessons on understanding functions. Click here to view all function lessons.

A function is a relationship between two variables. The first variable determines the value of the second variable. The value of the first variable corresponds to one and only one value for the second variable. Yes, I know that these formal definitions only make it more confusing.

Let's take a look at this another way. I always go back to my elementary years when we learned about functions - but never called them functions. We had what was known as an "in and out box".

Some teachers now call it a "Function Box" and this is why:. Here's a picture of an algebra function box. Imagine the equation being the center of the function box. You put a number in, the function box performs the calculation and out pops the answer. Let's take a look at an example with an actual equation.

Notice how our equation has 2 variables x and y. When we input 3, the function box then substitutes 3 for x and calculates the answer to be 7. No other number will correspond with 3, when using this equation. If you input another number such as 5, you will get a different output. No other number can correspond with 5, when substituting into this equation. Therefore, this equation can be labeled a function. It seems pretty easy, right? It seems like all equations would be considered functions.

Take a look at an example that is not considered a function. When we input 4 for x, we must take the square root of both sides in order to solve for y. Therefore, this does not satisfy the definition for a function: "the value of the first variable corresponds to one and only one value for the second value". We have more than one value for y. Hopefully with these two examples, you now understand the difference between an equation that represents a function and an equation that does not represent a function.

You will find more examples as you study the lessons in this chapter. So, what kinds of functions will you study? In Algebra 1, we will study linear functions much like linear equations and quadratic functions. As you progress into Algebra 2, you will be studying exponential functions.

Below is the table of contents for the Functions Unit. Click on the lesson that interests you, or follow them in order for a complete study of functions in Algebra 1. Click here for more information on our affordable subscription options.If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos.

Not feeling ready for this? Check out Get ready for Algebra 2. Course summary. Polynomial arithmetic. Intro to polynomials : Polynomial arithmetic Average rate of change of polynomials : Polynomial arithmetic Adding and subtracting polynomials : Polynomial arithmetic.

Multiplying monomials by polynomials : Polynomial arithmetic Multiplying binomials by polynomials : Polynomial arithmetic Special products of polynomials : Polynomial arithmetic. Complex numbers. The imaginary unit i : Complex numbers Complex numbers introduction : Complex numbers The complex plane : Complex numbers. Adding and subtracting complex numbers : Complex numbers Multiplying complex numbers : Complex numbers Quadratic equations with complex solutions : Complex numbers.

Polynomial factorization. Factoring monomials : Polynomial factorization Greatest common factor : Polynomial factorization Taking common factors : Polynomial factorization.

Factoring higher degree polynomials : Polynomial factorization Factoring using structure : Polynomial factorization Polynomial identities : Polynomial factorization Geometric series : Polynomial factorization.

Polynomial division. Dividing polynomials by x : Polynomial division Dividing quadratics by linear factors : Polynomial division Dividing polynomials by linear factors : Polynomial division. Polynomial Remainder Theorem : Polynomial division.

Polynomial graphs. Zeros of polynomials : Polynomial graphs Positive and negative intervals of polynomials : Polynomial graphs End behavior of polynomials : Polynomial graphs.

Putting it all together : Polynomial graphs. Rational exponents and radicals. Equivalent forms of exponential expressions : Rational exponents and radicals Solving exponential equations using properties of exponents : Rational exponents and radicals.

Exponential models.

functions algebra 2 ppt

Interpreting the rate of change of exponential models : Exponential models Constructing exponential models according to rate of change : Exponential models Advanced interpretation of exponential models : Exponential models. Introduction to logarithms : Logarithms The constant e and the natural logarithm : Logarithms Properties of logarithms : Logarithms.

The change of base formula for logarithms : Logarithms Solving exponential equations with logarithms : Logarithms Solving exponential models : Logarithms. Transformations of functions. Shifting functions : Transformations of functions Reflecting functions : Transformations of functions Symmetry of functions : Transformations of functions Scaling functions : Transformations of functions.

Putting it all together : Transformations of functions Graphs of square and cube root functions : Transformations of functions Graphs of exponential functions : Transformations of functions Graphs of logarithmic functions : Transformations of functions.

Cube-root equations : Equations Quadratic systems : Equations Solving equations by graphing : Equations. Unit circle introduction : Trigonometry Radians : Trigonometry The Pythagorean identity : Trigonometry Trigonometric values of special angles : Trigonometry. Graphs of sin xcos xand tan x : Trigonometry Amplitude, midline and period : Trigonometry Transforming sinusoidal graphs : Trigonometry Graphing sinusoidal functions : Trigonometry Sinusoidal models : Trigonometry.

Modeling with function combination : Modeling Interpreting features of functions : Modeling Manipulating formulas : Modeling. Modeling with two variables : Modeling Modeling with multiple variables : Modeling. Rational functions. Cancelling common factors : Rational functions End behavior of rational functions : Rational functions Discontinuities of rational functions : Rational functions Graphs of rational functions : Rational functions.

Modeling with rational functions : Rational functions Multiplying and dividing rational expressions : Rational functions Adding and subtracting rational expressions intro : Rational functions Adding and subtracting rational expressions factored : Rational functions Adding and subtracting rational expressions not factored : Rational functions.

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Products Sold on our sister site CrystalGraphics. Title: Algebra 2. Tags: algebra. Latest Highest Rated. Title: Algebra 2 1 Algebra 2 Section Linear Equations 2 What You'll LearnWhy It's Important To identify equations that are linear and graph them, To write linear equations in standard form, and To determine the intercepts of a line and use them to graph an equation.

You can write equations to represent relations in education, physics, and geology 3 Connection Physics You might guess that sound would travel fastest through air since air is less dense than other mediums like water, glass or steel. However, just the opposite is true. Sound travels though air most slowly of all. Through air it travels feet per second, through water about feet per second, and through glass and steel about 16, feet per second.

functions algebra 2 ppt

Since the value of y depends on the value of x, y is called the dependent variable, and x is called the independent variable.

In this graph the points appear to lie on a line. This graph is a function. The line would contain an infinite number of points, whose ordered pairs are solution of the equation y x. An equation whose graph is a line is called a linear equation. A linear equation is an equation that can be written in standard form Ax By C 7 Standard Form of a Linear Equation The standard form of a linear equation is Ax By C,where A, B, and C are real numbers and A and B are not both zero Usually A, B, and C are given as integers whose greatest common factor is 1 When variables other than x are used, assume that the letter coming first in the alphabet represents the domain or horizontal coordinate.

Identify A, B, and C. A function is linear if it can be defined by f x mx b, where m and b are real numbers.

functions algebra 2 ppt

In the definition of a linear function, m or b may be zero. The graph is a horizontal line. This function is called a constant function. If f x 0, the function is call the zero function.