AP Precalculus 1.1: Change in Tandem FULL LESSON and NOTES

DOWNLOAD THE NOTES FOR THIS LESSON HERE: https://drive.google.com/file/d/19bt9...

Please subscribe!    / nickperich  

AP Precalculus 1.1: Change in Tandem

Overview:
"Change in Tandem" describes how two quantities change together. In mathematics, we often look at how one quantity (called the dependent variable) changes in response to another (called the independent variable). This idea is important for understanding functions and how to read their graphs.

Key Terms and Definitions

Function Notation:
A function is a rule that assigns each input exactly one output.
Function notation looks like this:
f(x)

f is the name of the function.

x is the independent variable (input).

f(x) is the dependent variable (output), which depends on the value of x.

Independent and Dependent Variables:

Independent Variable: The input value that you choose or control. Example: time in hours.

Dependent Variable: The output value that changes depending on the input. Example: distance traveled.

Types of Change

Increasing Function:
A function is increasing when the output values get larger as the input values get larger.
In other words, as x goes up, f(x) also goes up.
On a graph, this looks like the line or curve going upward from left to right.

Decreasing Function:
A function is decreasing when the output values get smaller as the input values get larger.
As x goes up, f(x) goes down.
On a graph, this looks like the line or curve going downward from left to right.

Concavity

Concave Up:
A graph is concave up if it curves upward like a cup shape.
The rate of change is increasing.
The graph looks like it is bending upward.

Concave Down:
A graph is concave down if it curves downward like a frown.
The rate of change is decreasing.
The graph looks like it is bending downward.

Quick Summary Table

Increasing Function: Output goes up as input goes up (graph rises left to right)

Decreasing Function: Output goes down as input goes up (graph falls left to right)

Concave Up: Graph bends upward like a smile (rate of change is increasing)

Concave Down: Graph bends downward like a frown (rate of change is decreasing)

Example:
If a car is speeding up over time:

Time is the independent variable.

Speed is the dependent variable.

Since speed increases over time, the function is increasing.

If the speed is increasing faster and faster, the graph is concave up.

I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:

/ nickperich

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

#math #algebra #algebra2 #maths #math #shorts #funny #help #onlineclasses #onlinelearning #online #study