Properties of Functions and Basic Function Types: Toolkit Functions | Saylor Academy

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In this section, you will analyze graphs to determine whether they represent a function and be introduced to the graphs of the basic functions. Pay close attention to the basic functions because they will be referred to throughout most of the course.

Toolkit Functions

Source: Linda Green, https://youtu.be/4L7KxV-G4Fk
This work is licensed under a Creative Commons Attribution 4.0 License.

COURSE INTRODUCTION

Course Syllabus

Unit 1: Equations and Inequalities

1.1: Solving Linear and Rational Equations in One Variable

Solving Linear Equations in One Variable

Applications of Linear Equations

Rational Equations

1.2 Quadratic, Radical, and Absolute Value Equations

Complex Numbers

Solve Quadratic Equations by Factoring

Solve Quadratic Equations Using the Square Root Property

Using the Quadratic Formula and the Discriminant

Equations That are Quadratic in Form

Absolute Value Equations

Radical Equations

1.3: Linear Inequalities

Using Interval Notation and Properties of Inequalities

Solve Simple and Compound Linear Inequalities

Absolute Value Inequalities

Unit 2: Introduction to Functions

2.1: Notation and Basic Functions

The Rectangular Coordinate System and Graphs

Defining and Writing Functions

Properties of Functions and Basic Function Types

2.2: Properties of Functions and Describing Function Behavior

Finding the Domain of a Function Defined by an Equation

Finding Domain and Range from Graphs

Graphing Piecewise-Defined Functions

Calculate the Rate of Change of a Function

Determine Where a Function is Increasing, Decreasing, or Constant

Unit 3: Exponents and Polynomials

3.1: Composite Functions

Creating and Evaluating Composite Functions

Finding the Domain of a Composite Function

3.2: Transformations

Graphing Functions Using Vertical and Horizontal Shifts

Graphing Functions Using Reflections

Determining Whether a Function is One-to-One

Graphing Functions Using Stretches and Compressions

3.3: Inverse Functions

Inverse Functions

Unit 4: Linear Functions

4.1: Linear Functions

Representations of Linear Functions

Interpreting Slope as a Rate of Change

Writing and Interpreting an Equation for a Linear Function

Parallel and Perpendicualr Lines

4.2: Modeling with Linear Functions

Building Linear Models from Words

Modeling a Set of Data with Linear Functions

4.3: Fitting Linear Models to Data

Finding the Line of Best Fit

Unit 5: Polynomial Functions

5.1: Quadratic Functions

Understanding How the Graphs of Parabolas are Related to Their Quadratic Functions

Finding the Domain and Range of a Quadratic Function

Determining the Maximum and Minimum Values of Quadratic Functions

5.2: Power and Polynomial Functions

Power Functions

Polynomial Functions

5.3: Graphs of Polynomial Functions

Identify the x-Intercepts of Polynomial Functions whose Equations are Factorable

Graphing Polynomial Functions

5.4: Dividing Polynomials

Use Long Division to Divide Polynomials

Use Synthetic Division to Divide Polynomials

5.5: Finding Roots of Polynomial Functions

Three Techniques for Evaluating and Finding Zeros of Polynomial Functions

Using the Fundamental Theorem of Algebra and the Linear Factorization Theorem

Unit 6: Rational Functions

6.1: Characteristics of Rational Functions

End Behavior and Local Behavior of Rational Functions

Domain and Range of Rational Functions

Zeros of Rational Functions

6.2: Finding Asymptotes of Rational Functions

Vertical and Horizontal Asymptotes of Rational Functions

6.3: Graphs and Equations of Rational Functions

Graphing Rational Functions

Unit 7: Exponential and Logarithmic Functions

7.1: Intorduction to Exponential Functions