The Concept of a Function

Examples, videos, and solutions to help Grade 8 students learn that a function allows us to make predictions about the distance an object moves in any time interval.

New York State Common Core Math Grade 8, Module 5, Lesson 1

Worksheets for Grade 8

Lesson 1 Student Outcomes

• Students know that a function allows us to make predictions about the distance an object moves in any time interval. Students calculate average speed of a moving object over specific time intervals.
  
• Students know that constant reasoning involved.

Lesson 1 Student Summary

Functions are used to make predictions about real life situations. For example, a function allows you to predict the distance an object has traveled for any given time interval.

Constant rate cannot always be assumed. If not stated clearly, you can look at various intervals and inspect the average speed. When the average speed is the same over all time intervals, then you have constant rate. When the average speed is different, you do not have a constant rate.

Lesson 1 Classwork

Example 1
Suppose a moving object travels 256 feet in 4 seconds. Assume that the object travels at a constant speed, that is, the motion of the object is linear with a constant rate of change. Write a linear equation in two variables to represent the situation, and use it to make predictions about the distance traveled over various intervals of time.

Example 2
The object, a stone, is dropped from a height of 256 feet. It takes exactly 4 seconds for the stone to hit the ground. How far does the stone drop in the first 3 seconds? What about the last 3 seconds? Can we assume constant speed in this situation? That is, can this situation be expressed using a linear equation?

Exercises 1–6
Use the table to answer Exercises 1–5.

1. Name two predictions you can make from this table.
2. Name a prediction that would require more information.
3. What is the average speed of the object between zero and three seconds? How does this compare to the average speed calculated over the same interval in Example 1?

4. Take a closer look at the data for the falling stone by answering the questions below.
   a. How many feet did the stone drop between and second?
   b. How many feet did the stone drop between and seconds?
   c. How many feet did the stone drop between and seconds?
   d. How many feet did the stone drop between and seconds?
   e. Compare the distances the stone dropped from one time interval to the next. What do you notice?
5. What is the average speed of the stone in each interval seconds?
   Repeat this process for every half-second interval. Then answer the question that follows.
   a. Interval between 0 and 0.5 seconds:
   b. Interval between 0.5 and 1 seconds:
   c. Interval between 1 and 1.5 seconds:
   d. Interval between 1.5 and 2 seconds:
   e. Interval between 2 and 2.5 seconds:
   f. Interval between 2.5 and 3 seconds:
   g. Interval between 3 and 3.5 seconds:
   h. Compare the average speed between each time interval. What do you notice?
6. Is there any pattern to the data of the falling stone? Record your thoughts below.

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