Part a:

http://www.bespokeinvest.com/thinkbig/2012/1/4/ford-truck-sales-rise-for-second-straight-year.html

This business article shows Ford Inc. sales from 1992 to 2011.

The article includes a graph that indicates the function relationship between the sales over 19 years. This is because in the relation, y (sales) is a function of x (time or years). For each input x (ex: 2007, 2008, 2009), there is ONLY one distinctive output y (ex: 591k, 516k, 414k). However, it is possible to have the same output for more than multiple inputs but it is NOT possible to have multiple outputs for the same input.

However the function is not linear. This can be concluded through calculating the R.O.C. 

For 2007-2008, ROC is (-75) where for 2008-2009, ROC is (-102), and for 2009-2010 ROC equals (114).

So because ROC’s are different and do not increase or decrease at a constant rate, the function is not linear. 

The function has a mathematical model and may be written as S=f (t) where S represents the sales and t time.

Part b:

The relationship is not a function if a value in x-axis has no relation to the y-axis, or when a value in x-axis is related to more than one value in y-axis.  

In the article “Backup Software and Intel in SSDs”, there is a graph that displays the relationship between the product category (x-axis) and the company market leader (y-axis) of each product category. However, this is not a function since there are more than one distinctive output (ex: Intel, hp) for each input (processors, servers, SSD). For example, the processors’ category has two (outputs) companies’ market leaders which are hp and Intel.