Part a:
- 1. http://money.cnn.com/2010/02/02/news/companies/napster_music_industry/
- 2. Functions have exactly one output per input. They can be shown as a table, a table, a graph, or in words. A function also has pass the vertical line test where it can only touch a vertical line once.
- 3. This graph is a function because there is an output (dollars in millions) for every input (each year).
- 4. This function shows how each year the sales in the music industry has been falling since 1999. This article is slightly outdated, although CD sales have continued to fall since then. For every year (x value) the graph shows the sales in millions of dollars for that year (y value).
- 5. This graph is not a linear function because there is no ARC since the number by which the sales fall each year is not constant. The graph even showed a spike in sales around the mid 2000s showing that there is no constant slope.
- 6. N/A
- 7. The function is not linear because there is no average rate of change in the graph. While the article states that the average rate at which the sales have dropped over 10 years is 8%, the average rate of change is not constant from year to yearIf the function is not linear, explain in detail how you know it is not linear (be sure to refer to the average rate of change).
- 8. This function is not a mathematical model because the x inputs ( year) do not directly correlate to the y inputs (sales). That is to say that the y inputs could be any number and it would not make a difference.
Part b:
1.You could use the vertical line test to determine whether something is not a function. However, because functions can only have one output per input any table/graph that has more than one y value for an x value supplied is not a function.
2. http://blog.thecurrent.org/2014/02/40-years-of-album-sales-data-in-one-handy-chart/
3. This is a bar graph that shows music sales over the past 40 years (from 1973-2013) based on format (ie: CD, LP, Tape, 8 track, MP3).
4. This is not a function because if it we're either put into a line graph or a table, we would see that for every x value (input/year) there would be several y values (output/sales in millions of $) as this graph focuses on several music formats rise and decline of sales. For instance, we see earlier in the graph that sales for cassettes were MUCH higher then than CD, and in the 90's you can see that reverse.
1.You could use the vertical line test to determine whether something is not a function. However, because functions can only have one output per input any table/graph that has more than one y value for an x value supplied is not a function.
2. http://blog.thecurrent.org/2014/02/40-years-of-album-sales-data-in-one-handy-chart/
3. This is a bar graph that shows music sales over the past 40 years (from 1973-2013) based on format (ie: CD, LP, Tape, 8 track, MP3).
4. This is not a function because if it we're either put into a line graph or a table, we would see that for every x value (input/year) there would be several y values (output/sales in millions of $) as this graph focuses on several music formats rise and decline of sales. For instance, we see earlier in the graph that sales for cassettes were MUCH higher then than CD, and in the 90's you can see that reverse.
I really like how you mentioned how you used the vertical line test and how that helped you determine if it was a function. I also really liked the topic on the electronics since its a really relatable topic.
ReplyDeletealli,
ReplyDeleteyour first example is a good and your explanations are well detailed. it would have been good to show the rate of change calculations when explaining that the function was not linear, but other than that, good job! the second example actually shows many different relationships that are all functions. so, it's not an example of a non-function.
also, you'll lose some points since this was more than a week late. good job, though.
professor little