This question could be called Linear vs Exponential as it asks for linear with fancy wording: “equal difference over an equal interval”(as opposed to just the word linear)
(I) 3.5 cm a day would make the y values go up 3.5 each day this is linear
(II) depreciate 15% a year is exponential
(III) tripling is exponential
see #25 on this Regents for long answer of linear or exponential!!
This is a transformation both horizontal and vertical translation or moving!
The – 2 moves down the entire graph by 2 as it is faithful and does what we think it will do
Only answers (1) and (3) have been moved down
But the (x + 1) part is the horizontal shift and does the opposite of what it looks like so it will shift left
The easiest way to do this is to pick a point on the original graph like (2,3)
Move it one unit left and two units down to (1,1)
Which of the two graphs for answers (1) and (3) go through (1,1)?
From the Jan 2016 Common Core Algebra I Regents:
The level of challenge on the Regents like any exam varies quite a bit.
After posting about #1-19 of the Jan 2016 Common Core Algebra I Regents, challenge level is being added to each problem.
Please comment if you feel a problem is misclassified as I am only right about 80% of the time. Most importantly, students need to know what they find easy medium hard (often abbreviated as EMH)
click on the word easy for blog posts for Jan 2016 1 3 4 5 8 9 12 15 16
click on the word medium for blog posts for Jan 2016 2 7 13 14 17 18 19
click on the word hard for blog posts for Jan 2016 6 10 11 20
from the January 2016 Common Core Algebra I Regents
No solving necessary!! Just looking for the equation!!
Students need to remember how to find the area of a rectangle: length by width
What was the original area of the patio? The original area was 120 sq ft (10 x 12)
What is 50% more than 120? Add 1/2 of 120 which is 60 making the new area 120 + 60 = 180 leaving answers (2) and (3).
Since we are adding x amount to each dimension 10 becomes 10 + x and 12 goes to 12 + x.
Those two multiplied together = 180 and voila there it is!
From the January 2016 Common Core Algebra I Regents
Read this question carefully: How much is 2 subtracted from 10? 10-2
Apply that to the problem above and we need to do:
5x^2 – (2x – 3)^2
We will need to FOIL (or double distribute) the (2x – 3)^2
(2x – 3) (2x – 3)
F: (2x)(2x) = 4x^2
O: (-3)(2x) = -6x
I: (-3)(2x) = -6x
L: (-3)(-3) = 9
combine the like terms of -6x and -6x for -12x
4x^2 -12x +9 and subtract it from 5x^2 so it really looks like this:
5x^2 – (4x^2 – 12x +9) and the negative is distributed in the next line
5x^2 – 4x^2 + 12x – 9 then combine like terms and you have
x^2 + 12x – 9
match this up carefully — the answers look super similar
We could also use the TI-84 with Y1 for the original and Y2 for the answer choices
see below for answer choice (1) this is NOT a match as the tables list different y values for the same x values and there are clearly 2 different graphs (red and blue)
Let’s try answer choice (2) see below also NOT matching up as the tables list different y values for the same x values and there are clearly 2 different graphs (red and blue)
ok onto answer choice (3) and look at the table for same values in Y1 and Y2!!!
Unfortunately the TI-84 graph does not show the overlap of Y1 and Y2 in answer choice 3 but at least we do not see e can see that there are not 2 different functions being graphed