Function Sign, Rate of Change, and Concavity Vocab
Keeping straight the difference between functions being positive and rates of change being positive and functions increasing and rates of change increasing and functions being concave up can be hard at first but easy once we get good at it. This applet is modelled after the language used on the released practice exams. It presents functions of all the types that will be seen throughout AP Precalculus
- Level 1: Excludes asking about the function being positive or negative. Only asks about f(x) increasing vs decreasing and concave up vs concave down. But it asks it with a few styles of wording ("f(x) is increasing and the graph of f(x) is concave down" = "the rate of change of f(x) is positive and decreasing" = "f(x) is increasing at a decreasing rate")
- Level 2: This applet adds in questions that ask about the sign of f(x). An answer here may be "f(x) is positive and decreasing" which is of course a different thing than "the rate of change of f(x) is positive and decreasing.
I think this image of ways we describe functions and this image of ways we describe rates of change help things click. These images are the Rosetta Stone showing the same messages in two different languages, allowing us to learn how to translate between the language of "f(x) is" and the language of "the rate of change of f(x) is."
FRQ 3(C)
FRQ 3 is inherently a Unit 3 questions. But part (C) of it relies on Unit 1 vocab
- Part (i): The wording of the answer choices is identical to the exam.
- Part (ii): To the best of my knowledge, the wording here would get full credit on the AP exam.
- Parts (i) and (ii) mixed
End Behavior
The wording in this applet matches that of FRQ 1. Note: this applet is meant to encourage understanding of end behavior without a calculator even though FRQ 1 is a "calculator active" question.
Rational Functions
Marilyn Carlson says that a statistically significant reason students lose interest in math is that they come to see it as a set of procedures to memorize (I'm paraphrasing). Math is a language, math is an art, and math is a puzzle. Math is about making, discovering, and breaking rules. Pretty please don't let any of these applets lead you to the belief that math is about memorizing sets of rules.