Check out the y values…they are always positive and head towards zero but will never become zero. So y is greater than zero — please see the graph below: the graph looks like it hits the x-axis but never actually will as the small y values get super teeny but never hit zero.
From the January 2016 Common Core Algebra I Regents
According to www.regentsprep.org:
“Recursion is the process of choosing a starting term and repeatedly applying the same process to each term to arrive at the following term. Recursion requires that you know the value of the term immediately before the term you are trying to find.”
This question is all about notation. Recursive means what happens to each number so that it becomes the next number in the sequence.
How can we get from 3 to 7 and then from 7 to 15? and then from 15 to 31. Each new number in pink is just a little bit more than double the previous number. Look carefully at all four choices — only one of them is close to multiplying by 2.
f(1) = 3 means that the first number of the sequence is 3 which appears in all 4 answers.
f(n + 1) means the next number in the sequence.
Find the one that matches the given pattern :)
From the January 2016 Common Core Algebra I Regents
Notice we are looking for the x value — similar to #1 on this very same Regents!!
https://mathconfidence.com/2016/05/02/get-the-math-and-get-the-points-notice-x/
Input both equations into Y=…absolute value is found either under Math, Number or in the catalog which can be found by doing 2nd zero
For answer choice (1), when x = -2 both Y1 and Y2 are the same :)
For answer choice (2), when x = 2, Y1 = 4 while Y2 = 2
For answer choice (3), when x = 3, Y1 = 4.5 while Y2 = 3
For answer choice (4), when x = -6, here’s another snapshot with the table arrowed up to more negative numbers:
when x = -6, Y1 = 0 while Y2 = 6.
From the January 2016 Common Core Algebra I Regents
This is 2 points easily earned with a TI-84 while learning about the different types of
functions through comparing and contrasting. We need to check the xy table of each function and see if it matches the given table.
Below is answer (1) not a match. By the way, check out the change in y — linear!!
Below is answer (2) also not a match. Check out the change in y — linear!!
Onto answer choice (3) see below, um also not a match
And last but certainly not least, answer choice (4) see below: 2 points!!!!!
There are many extensions to this question!!
Linear vs exponential vs cubic in an equation and in a table
Use the TI-84 and also look at the equations to categorize the types of functions.
Two are linear as they look like y = mx + b and will graph in a line.
One of the functions is a power function and one is exponential.
Looking at rate of change of the xy table
Substituting in values of x into each equation to see if they make the equation true
The easiest x value to substitute is usually 0 so try it here and see if the y or f(x) value = 1 as shown in the table
From the January 2016 Common Core Algebra I Regents:
p is the number of people — which must be positive leaving answers (1) and (2).
What is an integer? Integer is related to the word integrity which means whole.
Real numbers means all numbers including non-integers like 1.5 — you cannot have 1.5 people
Math Confidence by Robin the Math Lady 