About This Chapter
Interpreting, Analyzing & Graphing Functions - Chapter Summary
Top instructors have developed entertaining lessons you can review or learn more about interpreting, analyzing and graphing functions. Explore these lessons from home or on-the-go to learn how functions are graphed and analyzed. Also, examine properties of functions, the rate of change, piecewise functions and more. By the end of this chapter, you will have the knowledge to:
- Plot points on a graph's Cartesian plane
- Compare linear and quadratic functions
- Examine a graph, table or function and describe the relationship
- Draw the graph of a function based on its qualitative features
- Analyze the graphs of rational functions, and determine the rate of change of a function
- Compare properties of functions algebraically, graphically and numerically
- Graph square root, cube root and piecewise functions
Watch fun video lessons and read engaging texts in this chapter at the pace that you choose. Revisit them often until you fully grasp the process of interpreting, analyzing and graphing functions. Assess your understanding with help from short multiple-choice quizzes and a chapter exam. Any questions you have about lesson topics can be submitted to our experts.
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. Comparing Graphs of Quadratic & Linear Functions
In this lesson, we will discuss the basics of linear and quadratic functions and their graphs. We will see some examples and discuss how to graph each type when given an equation.
3. Describe the Functional Relationship Between Quantities
In this lesson, you'll learn how to look at a graph, table, or function written mathematically and verbally describe the functional relationship shown. For example, you'll learn to describe whether the function is increasing or decreasing.
4. Draw a Graph Based on the Qualitative Features of a Function
Learn how to sketch the graph of a function based on a description of its behavior. You can do this even if you don't know any exact numbers for the input or output values!
5. Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range
A rational function arises from the ratio of two polynomial expressions. The graphs of rational functions often have distinct characteristics. In this lesson, we look at how to analyze some of those characteristics.
6. Determine the Rate of Change of a Function
In this lesson, we will learn about the rate of change of a function with specific focus on linear and exponential functions while examining the graphs of both types of functions.
7. Compare Properties of Functions Algebraically
In this lesson, we will explore algebraic and numeric properties and the evaluation of functions. We'll demonstrate function evaluations and the idea that every element of the domain has a unique element in the range.
8. Compare Properties of Functions Graphically
In this lesson, we will cover the characteristics of graphs of functions. We will employ the vertical line test and understand why some graphs do not qualify as functions.
9. Compare Properties of Functions Numerically
Can you compare functions when they're written out numerically as tables of values? In this lesson, you'll learn to do just that and to compare one function as a table to another written in a different form.
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.
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Other chapters within the NY Regents Exam - Algebra I: Test Prep & Practice course
- Algebraic Units & Modeling
- Structure of Mathematical Expressions
- Polynomial Operations Basics
- Creating Equations, Inequalities & Expressions
- Solving & Graphing Equations & Inequalities
- Understanding Data Using Statistics
- Interpreting Linear Models
- Understanding Functions
- Building Linear & Exponential Functions
- Basics of Rational & Irrational Numbers
- Quadratic & Polynomial Equations
- About the NY Regents Examinations
- NY Regents Exam - Algebra I Flashcards