Behavior of a Function Around Its Zeros
You are given test points to determine the behavior of a function.
We determined how to find zeros for different functions. Throughout the process, you should have noticed how important the zeros and a number line have been in identifying the behavior of a function.
In this Precalc course, the "zero method" will help you identify important behaviors of a function:
Understanding the behavior of a function around its zeros and asymptotes, finding max and min points, increasing and decreasing intervals, and concavity. This process will apply to Calculus, but you will look at the change rather than a static (stationary or motionless) environment.
Additional information
Calculus - You will learn about derivatives and how they are used to determine the behavior of a function.
You will look at the rate of change, i.e., "What is the rate of change of the area of the circle when the radius = a given value?"
The derivative is the rate of change of one variable "with respect" to another variable. i.e., what is the equation of the tangent line at a given point?
Derivatives will help you determine where the function is increasing/decreasing, where the max/min points are, and its concavity. You will study how things move, grow, travel, and expand. Change over time.
***The derivative's zeros will be identified as "critical points."***
Precalc - We're not interested in the rate of change (slope of a tangent line) and its effect.
We need to generate the equation of the function given its graph, graph a function w/o using a grapher, and be able to interpret a function's graph and its behavior around the zeros (and vertical asymptotes),
Q: Why is it so important to understand the function's graph behavior?
Let's assume you are given a function's graph without the function's equation, and asked to find the function's equation. How are you going to do that? (You already have the "know-how" and the previous lessons and activities have offered a beginning!)
Q: Why do you need to know how to graph a function without a grapher?
Simply because it is part of this course, and it's fun to be able to graph a function without using that grapher! It increases "brain power!"
(A little note: In some of these lessons, I might have identified the zeros as "critical points." This is incorrect. Teaching calculus is still instilled in me, and it sometimes "pops up."
Just ignore my errors, and remember to refer to all zeros as zeros, not critical points!)