About This Chapter
Standard: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (CCSS.Math.Content.8.F.A.2)
About This Chapter
A solid understanding of this standard can help students evaluate functions for a given value. Students who comprehend the methods required to make comparisons can look at functions in different forms, such as a table of values, an algebraic expression or a graph, and determine which function has a larger y-intercept or greater slope.
The lesson topics for this standard include:
- Comparing function properties algebraically
- Comparing properties of functions on a graph
- Comparing function properties numerically
You'll know your students grasp these concepts when they understand that there is just one output for every input in an algebraic function and can make comparisons of functions that are represented by a description or table. These standards and lessons can prepare students for high school and college math courses.
How to Use These Lessons in Your Classroom
Below are suggestions indicating how you could include these lessons in your regular curriculum to help you meet Common Core standards.
Function Comparison Lessons
Assign the video lessons on comparing properties of functions as homework or watch them in class. Design an algebraic representation of a function and a graph of function and present to your students. Have them compare the relationships between the y-intercepts and determine if the rate of change is the same for each.
Evaluating Expressions Lessons
Watch lessons on comparing properties of functions in class. Write an algebraic expression and have students evaluate it to determine the outcomes.
Pre-Quiz and Post-Quiz Lessons
Have students take the quizzes on comparing properties of functions to become familiar with these concepts. Watch the video lessons and then have students take the quizzes again to see how well they comprehended the information.
1. 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.
2. 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.
3. 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.
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Other chapters within the Common Core Math Grade 8 - Functions: Standards course