1. http://www.cnbc.com/id/101762773
2. To determine if a relationship is a function one must pass the vertical line test. To pass the test there must be only one input per output value.
3.
4. This graph shows the relationship between the total amount of charitable donations from 1973-2013.
5. The relationship does not appear to be a linear function because there is not an average rate of change throughout. Meaning there is no constant slope for the graph. However it does pass the vertical line test therefore it is a function, just not a linear one.
6. Not Applicable
7. For a function to be linear it has to have a constant rate of change. To find the rate of change you use the equation y2 - y1 / x2 -x1. You then apply this equation to every point set given, if each point has the same rate of change (or slope), than you know it is a linear function. In other words you use the equation to solve for the average rate of change which will give you the slope of the whole function.
8. The function is not a mathematical model because the amount of money given to charity is not determined by the year. The year is only an indicator for when an amount was given. As the years progress the amounts do not grow or decrease in accordance.
Part 2
1. The criteria for determining when a relationship is NOT a function is when the relationship does not pass the vertical line test. That means that there is more than one output for every input
2.
3. This relationship shows the obesity rate based on the percentage of people who drive or carpool.
4. This is not a function because there is not one output value per input value, there are many. Each of the blue dots represents a person, and based on the same percentage of the time that some people drive they are not all the same obesity. Therefore there are multipul obesity rates per percentages of driving and carpooling.
Great explanation of linear function!
ReplyDeletevery well done. perfect explanation of what is and is not a function.
ReplyDeleteHey Sarah! Thought you did a great job on your blog post. I was particularly impressed by your second graph, illustrating the obesity rate and the percentage of commuters who drive to work. Supplies a sort of uncomfortable reality! I, too, detailed the formula for the average rate of change in my answer for Part A, Number 7. I was glad to see you included it as well :)
ReplyDeletenice job, on both examples, sarah! the only thing that i would add to your first example is to show that the calculations prove that the function is not linear, as you explained it so well. also, you were supposed to use function notation when explaining the math model part. other than that, great work! your second example is spot on!
ReplyDeleteprof little