Math Mammoth Introduction to Functions

61 pages
(includes answers)

Sample pages (PDF)
Contents
Rate of Change
Linear vs. Nonlinear Functions
Describing Functions 2

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Math Mammoth Introduction to Functions is a worktext that covers various introductory topics from the theory of functions, following the Common Core Standards (CCS) for 8th grade (specifically, the standards 8.F.1, 8.F.2, 8.F.3, 8.F.4, and 8.F.5). These topics prepare students for studying functions in great detail in high school math, and even include preparatory ideas for calculus (rate of change).

The first lesson focuses on the basic definition of a function, as a relationship between two sets that assigns exactly one output for each input. It also briefly explains the range and domain of a function, even though those terms are not required in the CCS.

Next, we study the rate of change in the context of linear functions. Students calculate the rate of change from functions given as a table of values or from their graphs. They also encounter nonlinear functions and calculate the rate of change for those in specific intervals.

Then, students learn about the initial value of a function (its value when the input is zero), and learn that the equation y = mx + b defines a linear function. They write and plot equations of that form to model linear relationships. We also spend one lesson looking at linear versus nonlinear relationships.

The following major topic is describing functions. Students analyze a graph and tell whether a function is increasing, decreasing, or constant; linear or nonlinear. They sketch a graph matching a given verbal description, and interpret given graphs of nonlinear functions in a variety of the real-life contexts.

Lastly, students compare properties of two functions represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, distance as a function of time is given as an equation for one airplane, and as a graph for another, and students answer questions concerning the speed and distance of the two airplanes.

The answers are appended.

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.