# Formal Definition of a Function

Video solutions to help Grade 8 students know that a function assigns to each input exactly one output.

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Lessons for Grade 8
Common Core For Grade 8
## New York State Common Core Math Module 5, Grade 8, Lesson 2

Lesson 2 Student Outcomes
• Students know that a function assigns to each input exactly one output.

• Students know that some functions can be expressed by a formula or rule, and when an input is used with the formula, the outcome is the output.

Lesson 2 Student Summary
A

__function__ is a rule that assigns to each input

__exactly one output__. The phrase “exactly one output” must be part of
the definition so that the function can serve its purpose of being predictive.

Functions are sometimes described as an input-output machine. For example, given a function the input is time
and the output is the distance traveled in seconds.

Lesson 2 Classwork
Shown below are the table from Example 2 of the last lesson and another table of values. Make a conjecture
about the differences between the two tables. What do you notice?

Exercise 1

1. Let y be the distance traveled in time t. Use the function y = 16t

^{2} to calculate the distance the stone dropped for
the given time t.

a. Are the distances you calculated equal to the table from Lesson 1?

b. Does the function y = 16t

^{2} accurately represent the distance the stone fell after a given time ? In other
words, does the function assign to the correct distance? Explain.

Exercises 2–5

2 - 4. Can the table shown below represent a function? Explain.

5. It takes Josephine 34 minutes to complete her homework assignment of 10 problems. If we assume that she works
at a constant rate, we can describe the situation using a function.

a. Predict how many problems Josephine can complete in 25 minutes.

b. Write the two-variable linear equation that represents Josephine’s constant rate of work.

c. Use the equation you wrote in part (b) as the formula for the function to complete the table below. Round
your answers to the hundredths place.

After minutes, Josephine was able to complete problems, which means that she was able to complete
problem, then get about halfway through the next problem.

d. Compare your prediction from part (a) to the number you found in the table above.

e. Use the formula from part (b) to compute the number of problems completed when x = -7. Does your
answer make sense? Explain.

f. For this problem we assumed that Josephine worked at a constant rate. Do you think that is a reasonable
assumption for this situation? Explain.