The 3rd graph (the one on the right) is not a function as a vertical line passes through twice.
The idea of a function vs not a function is mostly important for calculus although the curriculum did not used to focus on this. One of the reasons that Math has adopted this topic is that a calculator will not help with this type of problem. So look at Marcel’s graph: if you draw a vertical line at x = 2, it will hit the graph twice and therefore this is not a function. Do you hear Staples saying “That was easy”?
So Marcel is not correct as this is not a function as it fails the vertical line test! Hooray you just got 2 more points!!!
How to help your students pass the Regents, your son or daughter, niece or nephew, or yourself.
This is a series to help students pass the Regents and graduate high school while learning some Math in the process
For most students, the Math Regents they will focus on is Common Core Algebra I but we will also discuss Common Core Geometry.
Ready for Learn, Pass Graduate??
The Common Core exams are much harder than the old ones and students will need
1. more practice
2. more content knowledge
3. more content exposure
4. more motivation
Are you ready? See below for the first installment: January 2016 long answer #25:
This is an easy problem!!
Students should be able to see that for every increase of 2 in x the y value is going down by 2.5 and therefore the function is linear
Here is a model response from the model response set from http://www.nysedregents.org/algebraone/116/algone12016-mrs.pdf
Another easy way is to draw it (again from the Model Response Set)
This is worth 2 points folks and it’s an easy 2 points so make sure you review.
It is also not exponential because it does not have a pattern like an exponential — here is an example of an exponential pattern of y = 2^x: 1, 2,4, 8, 16 each number in the sequence is double the number before. The pattern has a constant multiplier, while our list of 10, 7.5, 5, 2.5, 0 has a constant rate of change of -2.5 which means it is a linear function or a line!!
When putting the answer choices into the TI-84 we can see that the only match is II.
Analyzing a graph can teach students about the zeros or solutions of a function. This function passes through the x-axis 3 times: at x = -2, x = 1 and x =3. We can also use this question to talk about factoring, y-intercepts, end behavior and other cool Math ideas. The process of elimination is very rewarding as compare/contrast is a great way to learn content and metacognition.
I am in favor of students knowing the Math part of this for sure but with the TI-84 , they can get the Math and get points. The 2 points on this type of question may make the difference between Pass and Fail and perhaps even high school graduation. The problem below comes from the June 2015 Algebra I Regents.
Option I is a NO GO so answers (1) and (3) are OUT.
Rigor? Or graduation rate? Hmmm.. this has been the debate for the Algebra Regents for many years.
If seniors need a Regents for graduation, the bar cannot be set too high, which has been the reason that Integrated Algebra Regents/Math A etc have not had high intensity. BUT this year all the seniors were taking ye olde Integrated Algebra and most of the Common Core takers were 8th and 9th graders. Wondering if this will get easier as this year’s freshmen approach their 2018 graduation date.