Inspired by this tweet:

Looking at our latest Algebra I Regents, here in NY, here is a great example of the use of a graphing calculator and compare/contrast/use metacognition:

All 4 answer choices have a 3 but in different and important places!!

First question, does this xy table look like it is for a linear function?

We can look at the equations and see which f(x) = mx + b

We can also use the TI-84 and check the table to see if it matches the table above!

Let’s go to the graphing calculator:

Answer choice (1) below: this is linear and is clearly not a match especially since the rate of change is always 3 (every time x goes up by 1 y goes up by 3)

Answer choice (2) below is also linear as it has a constant rate of change…not a match:

Answer choice (3) is shown below and, well, we’re still lookin’:

Answer choice (4) is below!!

2 points!!

These answers choices can be used to compare/contrast similarities and differences in their parent functions (linear, cubic and exponential).