Mat126 Week 3 Functions

Week 3 Discussion 1

Part 1

1. In your own words, define the word “function.”

A function is a relation between a set of input and output values to determine the domain and range of the function. In order for a relation to become a function each input must map a single output.

2. Give your own example of a function using a set of at least 4 ordered pairs. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and 5. Your example should not be the same as those of other students or the textbook. There are thousands of possible examples.

(2, -12), (3, 1), (5, 0), (7, 1), (9, 2)

3. Explain why your example models a function. This is extremely important for your learning.

In the example, each value in the domain maps to a single value in the range. It is okay for two inputs to map to the same output. So 3 can map to 1 and 7 can map to 1. But it is not okay for an input to map to two *different* outputs.

4. Give your own example of at least four ordered pairs that does not model a function. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and +5. Your example should not be the same as those of other students or the textbook. There are thousands of possible examples.

(2, -12), (2, 0), (3, 1), (5,2), (7, -12), (9,2)

5. Explain why your example does not model a function.

This does not model a function because the same input 2 results in different outputs of -12 and 0. A function must only map the inputs to a single output value, not multiple output values for the same input.

Part 2

1. Select any two integers between -12 and +12 which will become solutions to a system of two equations.

x = 0 and y = 5

2. Write two equations that have your two integers as solutions. Show how you built the equations using your integers. Your solution and equations should not be the same as those of other students or the textbook. There are infinite...