Unit 1 of Welcome to the Graphs of Life: Graphing Functions
Intro
What if I were to tell you that we could create machines which make ordered pairs according to our whims and wishes? These machines use a predetermined program - a relationship between the coordinates. If you give the machine an x coordinate, it will give you a y coordinate. Each x coordinate is given its own y coordinate by the machine, and we can match the x coordinate with the y coordinate to create an ordered pair. Some of these machines are programmed to spit out y coordinates that match the graphs we need. Need a graph for how fast water heats up as time goes by? The machine will create the graph for you. It turns out that there is a way to code each graph, a program that creates each points based on minimal information. These machines are called functions, and they look like this: "y=x+2". It might seem strange, but the little math equation "y=x+2" creates an entire graph. Let us discover how. First we will examine functions that create graphs of lines, and later on we will examine a strange creature called a "parabola".
Objectives
1. You will be able to produce the graphs of certain equations.
2. You will be able to understand which functions generate parabolas and lines.
3. You will be able to find and understand key features of parabolas and lines.
4. You will be able to describe graphs using functions of parabolas of lines.
Day 1: From Functions of Lines to Graphs of Lines
From Functions of Lines to Graphs of Lines
Day 2: Key Features of Graphs of Lines
Key Features of Graphs of Lines
Day 3: From Graphs of Lines to Functions of Lines
From Graphs of Lines to Functions of Lines
Day 4: From Functions of Parabolas to Graphs of Parabolas
From Functions of Parabolas to Graphs of Parabolas
Day 5: Key Features of Graphs of Parabolas
Key Features of Graphs of Parabolas
Day 6: From Graphs of Parabolas to Functions of Parabolas
From Graphs of Parabolas to Functions of Parabolas
Reflection
What have you learned in this unit? How do functions relate to graphs? How might this knowledge of functions and the graphs they generate be useful knowledge?