About This Chapter
Standard: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values.
About This Chapter
Students who have mastered this standard are proficient in combining two or more functions. Students understand they may substitute variables, numbers or other functions.
Lessons in this standard cover concepts such as:
- Understanding basics of function notation
- Tips for composing functions
- Strategies for various ways to graph linear equations
- Understanding rate of change and initial values of functions
Students demonstrate mastery of this standard when composing functions by beginning with the outside function. They are also proficient in evaluating the composition of functions at specific values. Mastery of this standard supports their college and career readiness because being able to model linear relationships is an important foundational skill for upper level math. In addition, working with mathematics encourages students' higher level thinking skills.
How to Use These Lessons in Your Classroom
Pretest/Posttest Composing Functions Lesson
Ask students to complete the quiz in the How to Compose Functions lesson before viewing the video, as a way to check for prior understanding. Then share and discuss the video lesson. Ask students to complete the quiz for a second time, comparing their results to the pretest.
Initial Value Lesson
Share the video lessons concerned with determining the initial value of a function. Review math vocabulary, including initial condition, constant of integration, derivative, integral and antiderivative. Work through additional problem examples, and then assign a set of practice exercises to check for student understanding.
Rate of Change Lesson
Watch the video lessons pertaining to rate of change with your class. Review the problem examples. Assign an exercise to each student, asking individuals to teach their solutions to a small group after successful completion of the problems.
1. How to Compose Functions
Function composition is the process of putting two or more functions together. This video lesson will explain how this process works and also show you how to evaluate functions that have been composed.
2. Composing Functions: Definition and Examples
In this lesson, you'll learn the definition of a mathematical function and explore function notation and function tables. We will also review several examples of functions.
3. Model a Linear Relationship Between Two Quantities
In this lesson, we will learn about modeling linear relationships by converting domain and range values into ordered pairs and then constructing a graph.
4. 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.
5. Determine the Initial Value of a Function
In this lesson, you will learn to determine the initial value of a function by studying functions in the form of word problems, graphs and linear equations.
6. Interpret Rate of Change and Initial Value
In this lesson, you'll learn how to interpret the rate of change and initial value of a function. We'll also discuss applying these principles to word problems and in real-world situations.
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Other chapters within the Common Core Math Grade 8 - Functions: Standards course