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## Unit 8: Functions

About this unit.

A function is like a machine that takes an input and gives an output. Let's explore how we can graph, analyze, and create different types of functions.

## 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)
- 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)
- Function inputs & outputs: equation Get 3 of 4 questions to level up!
- Function inputs & outputs: graph Get 3 of 4 questions to level up!

## Functions and equations

- Equations vs. functions (Opens a modal)
- 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

- Intervals and interval notation (Opens a modal)
- What is the domain of a function? (Opens a modal)
- What is the range of a function? (Opens a modal)
- Worked example: domain and range from graph (Opens a modal)
- Domain and range from graph Get 5 of 7 questions to level up!

## Determining the domain of a function

- Determining whether values are in domain of function (Opens a modal)
- Examples finding the domain of functions (Opens a modal)
- Worked example: determining domain word problem (real numbers) (Opens a modal)
- Worked example: determining domain word problem (positive integers) (Opens a modal)
- Worked example: determining domain word problem (all integers) (Opens a modal)
- Identifying values in the domain Get 3 of 4 questions to level up!
- Determine the domain of functions Get 3 of 4 questions to level up!
- Function domain word problems Get 3 of 4 questions to level up!

## Recognizing functions

- Recognizing functions from graph (Opens a modal)
- Does a vertical line represent a function? (Opens a modal)
- Recognizing functions from table (Opens a modal)
- Recognizing functions from verbal description (Opens a modal)
- Recognizing functions from verbal description word problem (Opens a modal)
- Recognize functions from graphs Get 3 of 4 questions to level up!
- Recognize functions from tables Get 3 of 4 questions to level up!

## Maximum and minimum points

- Introduction to minimum and maximum points (Opens a modal)
- Worked example: absolute and relative extrema (Opens a modal)
- Relative maxima and minima Get 3 of 4 questions to level up!
- Absolute maxima and minima Get 3 of 4 questions to level up!

## Intervals where a function is positive, negative, increasing, or decreasing

- Increasing, decreasing, positive or negative intervals (Opens a modal)
- Worked example: positive & negative intervals (Opens a modal)
- Positive and negative intervals Get 3 of 4 questions to level up!
- Increasing and decreasing intervals Get 3 of 4 questions to level up!

## Interpreting features of graphs

- Graph interpretation word problem: temperature (Opens a modal)
- Graph interpretation word problem: basketball (Opens a modal)
- Creativity break: How can people get creative in algebra (Opens a modal)
- Graph interpretation word problems Get 3 of 4 questions to level up!

## Average rate of change

- Introduction to average rate of change (Opens a modal)
- Worked example: average rate of change from graph (Opens a modal)
- Worked example: average rate of change from table (Opens a modal)
- Average rate of change: graphs & tables Get 3 of 4 questions to level up!

## Average rate of change word problems

- Average rate of change word problem: table (Opens a modal)
- Average rate of change word problem: graph (Opens a modal)
- Average rate of change review (Opens a modal)
- Average rate of change word problems Get 3 of 4 questions to level up!

## Intro to inverse functions

- Intro to inverse functions (Opens a modal)
- Inputs & outputs of inverse functions (Opens a modal)
- Graphing the inverse of a linear function (Opens a modal)
- Finding inverse functions: linear (Opens a modal)
- Functions: FAQ (Opens a modal)
- Evaluate inverse functions Get 3 of 4 questions to level up!
- Finding inverses of linear functions Get 3 of 4 questions to level up!

## Upload a screenshot and solve any math, physics, or accounting problem instantly with MathGPT!

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- Solve equations and inequalities
- Simplify expressions
- Factor polynomials
- Graph equations and inequalities
- Advanced solvers
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- Arithmetics
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- Percentages
- Scientific Notation
- Inequalities

## What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

- The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
- The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
- The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
- The calculus section will carry out differentiation as well as definite and indefinite integration.
- The matrices section contains commands for the arithmetic manipulation of matrices.
- The graphs section contains commands for plotting equations and inequalities.
- The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

## Math Topics

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## Homework Helper: AI Math Solve 4+

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A great tool to help students learn new things, prepare for tests, and master subjects like math, chemistry, and physics. Unlike traditional tutoring services, our app doesn't just hand out answers - it guides students through each problem with detailed step-by-step explanations and solutions, empowering them to understand and solve similar problems on their own. Here's how our app helps you learn: Comprehensive help with homework. Whether you're solving algebraic equations or balancing chemical reactions, our app will give you the support you need to solve even the most challenging problems. Our application will help you cope with even the most complex tasks! Easy organization: With the ability to save completed tasks and questions in the app's file directory, students can easily return to their work to review, share it with classmates, or print it for reference. Cooperative Learning: Need more help? AI Homework Helper facilitates group learning by allowing users to work on math problems with friends, classmates and others, creating a collaborative learning environment. For those looking for unlimited access to our premium features, we offer a subscription service: Your iTunes account will be charged upon confirmation of purchase. Subscriptions are automatically billed according to the selected plan. Manage your subscription and turn off auto-renewal in Settings to maintain control of your membership. Subscriptions with a free trial period will transition to a paid subscription upon renewal. At AI Homework Helper we believe in empowering students to become confident and independent learners. Try our app today and discover the difference it can make in your academic journey. Privacy Policy: https://docs.google.com/document/d/1_5xd-bfOv8_3y3huQ64q0-NcKNFlpJT6aLiqrel15VI/edit Terms of Use: https://docs.google.com/document/d/1ceeWBb2GMjoYEs9gEVAnEIYgN1T0G7F-DCNWoiSrvYU/edit

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The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!

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