About This Chapter
Graphs of Algebraic Functions - Chapter Summary
These video lessons show you how graphs work in algebra. Our instructors explain what a number line is and show the parts of a graph. Other lessons look at graphing basic functions, inverse functions and functions of functions.
Polynomials functions are discussed here, as are exponentials, logarithms and the natural log. You will find out about horizontal and vertical asymptotes, as well as implicit functions. After completing all the lessons in this chapter, you should be prepared to:
- Describe a number line
- Name parts of a graph
- Plot points on the coordinate plane
- Graph a variety of functions
- Explain the properties of polynomials functions
- Understand exponentials and logarithms
- Describe slopes and tangents on a graph
- Show the equation of a line using point-slope formula
Our lessons are brief and entertaining, and all include self-assessment quizzes that enable you to check what you've learned. The timeline's jump feature allows you to quickly find topics in each lesson that you need to study a bit more. The lessons are all led by instructors who are experts in the field. If you need extra help, it's easy to contact them with your questions.
1. What Is a Number Line?
A number line is a visual representation of all real numbers. In this lesson, we'll learn how to identify points on a number line. We'll also practice addition and subtraction, letting the number line do all the hard work.
2. What Are the Different Parts of a Graph?
Being able to read a graph isn't just vital for an algebra class. Graphs and charts are used everywhere! We'll take a crash course on the basic x/y plane used in algebra and the fundamental vocab you need.
3. Plotting Points on the Coordinate Plane
If you'll be working with a graph, otherwise known as the coordinate plane, it's essential to understand how it works. This includes learning the parts of a graph, identifying points and plotting points.
4. Graphing Basic Functions
Graphs are just like maps - when you know the language! Review how locations have x and y coordinates similar to latitude and longitude, and how to plot points in the Cartesian plane.
5. Compounding Functions and Graphing Functions of Functions
We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!
6. Understanding and Graphing the Inverse Function
If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.
7. Polynomial Functions: Properties and Factoring
Everything from projectile motion to trigonometric functions can be described by polynomials. Review factoring, polynomials and quadratic functions in this lesson.
8. Polynomial Functions: Exponentials and Simplifying
How do we keep track of a rapidly multiplying population of bunnies? Well, those are simply powers of 2. Review powers and simplify problems with exponents in this lesson.
9. Slopes and Tangents on a Graph
Hit the slopes and learn how the steepness of a line is calculated. Calculate the slopes between points and draw the tangents of curves on graphs in this lesson.
10. Equation of a Line Using Point-Slope Formula
It's time for a road trip to Las Vegas, and after four hours of driving at 60 mph ... Are we there yet? Learn the point-slope form of the equation of a line to help answer this age-old question.
11. Horizontal and Vertical Asymptotes
No matter how hard you try to get to them, asymptotes remain out of reach. Learn about these invisible lines on graphs that show you places your equations just can't go.
12. Implicit Functions
Sometimes inputting a variable into a function 'black box' doesn't yield a simple output. Find out what happens when you can't isolate the dependent variable on one side of the equal sign.
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Other chapters within the Accuplacer Math: Advanced Algebra and Functions Placement Test Study Guide course
- Arithmetic with Rational Expressions
- Factoring in Algebra
- Expanding Polynomials
- Manipulating Roots
- Working with Exponents & Exponential Expressions
- Solving & Graphing Linear Equations
- Quadratic Equations
- Calculating & Graphing Inequalities
- Solving Systems of Linear Equations
- Geometric Angles & Shapes
- Line Theorems
- Similarity & Congruency in Geometry
- Pythagorean Theorem
- Understanding Exponential & Logarithmic Functions
- Trigonometric Functions & Equations
- Accuplacer Math: Advanced Algebra and Functions Placement Test Flashcards