About This Chapter
TASC Math: Graphing and Functions - Chapter Summary
Use the lessons in this chapter to prepare for the graphing and function questions that could appear on the TASC Mathematics test. As you work through the chapter's short and engaging lessons, you'll review the parts of a graph and study methods for graphing several types of functions. When you're finished with the chapter, you should be able to:
- Graph basic, inverse, piecewise, step, square root, cube root, absolute value and rational functions
- Evaluate compounding, polynomial and implicit functions
- Work with exponentials and horizontal/vertical asymptotes
- Find slopes and tangents
- Use the point-slope formula
- Analyze polynomial function graphs
This chapter contains short, engaging videos that are taught by experienced instructors. The videos include graphics and real-life examples. Lesson transcripts that emphasizes key terms are also available. After watching the videos, you can test your understanding through multiple-choice quizzes and an end-of-chapter test.
1. 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.
2. 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!
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. Graphing Square Root & Cube Root Functions
This lesson will briefly review the most basic square root and cube root functions. Then we will look at transformations of these basic functions and their corresponding algebraic operations that we can use to graph more involved square root and cube root functions.
11. How to Graph Piecewise Functions
Piecewise functions are specific functions that have more than one piece. There is a special trick to graphing these type of functions, which you will learn in this lesson.
12. How to Graph Step Functions
In this lesson, we'll learn the definition of a step function and two of its family members: floor functions and ceiling functions. We'll then look at how to graph step functions using two real world examples.
13. Graphing Absolute Value Functions
The purpose of this lesson is to define what is meant by the absolute value of a number and then to extend this idea to define the parent function of absolute value.
14. Graphing & Analyzing Rational Functions
After watching this video lesson, you will be able to graph a rational function by analyzing its horizontal and vertical asymptotes. Learn to find how the graph behaves around the asymptotes.
15. Analyzing Graphs of Polynomial Functions
This lesson will explain the graph of a polynomial function by identifying properties including end behavior, real and non-real zeros, odd and even degree, and relative maxima or minima. We will then sketch a graph using this information.
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Other chapters within the TASC Mathematics: Prep and Practice course
- TASC Math: Real Numbers
- TASC Math: Complex and Imaginary Numbers Review
- Intro to Algebraic Expressions
- Intro to Algebraic Equations
- TASC Math: Exponents and Exponential Expressions
- Overview of Square Roots
- TASC Math: Radical Expressions
- TASC Math: Functions
- Overview of Sequences
- TASC Math: Inequalities
- TASC Math: Algebraic Distribution
- TASC Math: Linear Equations
- TASC Math: Factoring
- TASC Math: Quadratic Equations
- TASC Math: Graphing and Factoring Quadratic Equations
- TASC Math: Properties of Polynomial Functions
- TASC Math: Rational Expressions
- TASC Math: Measurement
- Lines, Angles & Arcs
- Shapes in Geometry
- Volume & Surface Area
- TASC Math: Calculations, Ratios, Percent & Proportions
- TASC Math: Data, Statistics, and Probability
- Making Inferences & Justifying Conclusions in Math
- TASC Mathematics Flashcards