What's Your Function?

Section A

1. http://www.theatlantic.com/technology/archive/2012/03/the-missing-20th-century-how-copyright-protection-makes-books-vanish/255282/

2. A function is a relationship in which there is exactly one output per input. Functions may be represented as a graph, a table, a formula, or in words. A function must also pass the vertical line test. 

3. The following image is a function, as there is one output (books offered) per every input (by decade written).

4. This graph explains Amazon's efforts to increase its book supply. For each decade listed on the x-axis, there is one correlating numerical value on the y-axis that details the number of books available on Amazon from a certain decade. 

5. This graph is not a linear function, as there is no average rate of change to produce points that develop at a steady, increasing interval per value. As Amazon offers a different number of books available at each decade of literature, there is no average rate of change. However, this image is a function, as it passes the vertical line test. 

6. Does not apply.

7. A linear function must supply an average rate of change, indicating a steady increase for each interval on the graph. The average rate of change is found by using the formula, Y2-Y1/X2-X1. After plugging values into this formula, if there is a constant rate of change for each interval on the graph, then the image satisfies the requirements for a linear function. 

8. This graph is also not a mathematical model. The amount of books offered on the y-axis does not determine the year, or the amount of books offered. This graph merely represents the books offered for each time period, increasing in decades, but the two pieces of data are not reliant on each other for the next illustration. 

Section B

1. A relationship is not a function if there exists more than one y-value for every x-value supplied. A relationship that is not a function will also not pass the vertical line test, reinforcing the idea supplied in the sentence above. 

2. http://www.statista.com/chart/1068/samsungs-profit-soars-as-apple-falters/

3. This graph illustrates net profit growth of two powerhouse electronic companies, Samsung and Apple. The blue line indicates Samsung's profits. While the navy applies to Apple. 

4. This is not a function, as there are two y-values (profit percentages) per one x-value (quarterly report). At each quarter within the graph, there exists two values on the graph, comparing Samsung's profits to Apples'. For example, in the first quarter of 2012, Apple experienced profit margins of roughly 90%, while at the same time, Samsung accumulated net profit of 80%.