2. Functions have an output for every input and passes the vertical line test. The output has to be directly related to the input.
3. The article has several relationships that represent a function. There is a graph on unemployment and wage growth and a graph on household debt.
4. For the graph regarding household debt, there is an input for every output and it passes the vertical line test. For every input in the graph there is an output. For the percent of household debt, there is a corresponding year. Additionally, there is a relationship between the input and the outputs of the graphs.
5. The function is not a linear function
6. The function does not have a constant rate of change. At some points, the rate of change is positive and at some points it is negative which means it cannot be a linear function.
7. If 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. A mathematical model is a function used to describe an actual situation. However this graph is not a mathematical model because the time does not determine the household debt, the input has no real impact on the output. For example, a function with the equation U=unemployment T=Time F(U)=T would not be a function of this graph.
Part
b:
A relationship is not a function when it fails the vertical line test. Additionally, two numbers can be related and not be a function. For example two numbers can be a function to time but they are not functions to each other because they are not dependent on each other. http://www.rotoworld.com/articles/cfb/45952/349/out-of-the-box
Question 3/4
The charts compare the statistics of several rookie quarterbacks
in 2014. The charts compare the different pass completion percentage on
different types of passes and when the quarterbacks face pressure. There is no
real relationship between the statistics of each quarterbacl. There is also no
output for every input in the graph. It would be impossible to just input
pressure or blitz and generate an output. It is impossible to quantify the
amount of blitz a quarterback faces which means the output cannot be completely
dependent on the input. You would also need a quantifiable output for the
distance of a throw instead of just the completion percentage of throws of a
certain range.
This is interesting, how did you come across this idea?
ReplyDeleteGreat examples for the line graph and non function example.
ReplyDeleteReally great graphs and examples
ReplyDeletematthias,
ReplyDeleteyour first example is a good one and very interesting. your explanation of linearity is good, but it would have been nice to see calculations for ROC to show that it is in fact not linear. as far as your math model explanation goes, you are correct that it is not a math model, however, this relationship can be explained using function notation and you indicated that it cannot, which is incorrect.
in your second example you have two separate relationships, and i believe that they are both separate functions, as i don't see any repeated outputs per one input.
prof little