10.6.1 Graphs of Functions

Analysts in many different industries work very hard to analyze trends in data.  One of the best ways of visualizing these trends is with graphs.  Single graphs, or several graphs in conjunction, can help tell a story about what has happened or what might soon be happening.  Today, we will be thinking about what story a graph tells us and what possibilities it might suggest.

American Airilnes shares  regularly had low volumes of trading and a relatively stable share price.  In September of 2001, the value of the stock dropped dramatically during increased lelvels of trading amidst fears over the industry.  As those fears proved false, the value of the stock began returning to normal, share trading volume was still elevated as people saw an opportunity to buy the stock before it returned back to previous levels.

 What happened in 2001 that caused this dramatic drop in American Airlines share price?

What You Should Know after Today

  • describe a possible situation for a given graph
  • draw a possible graph for a given situation


  • Notes
  • Worksheets


  • p274 #1-6, 9, 10, 13, 14, *12, *15
  • Worksheet


FileDescriptionFile size
Download this file (10.6.1a.notes.pdf)10.6.1a.notes.pdfNotes: Part 13525 kB
Download this file (10.6.1a.worksheets.pdf)10.6.1a.worksheets.pdfWorksheet735 kB
Download this file (10.6.1b.notes.pdf)10.6.1b.notes.pdfNotes Part 23772 kB

10.6.2 Linear Functions

Functions show the relation between input (x) and output (y).  It is important to know some of the important terminology around functions. 

What you should know after today

  • explain why data points should or should not be connected on a graph
  • draw a graph from a set of data (ordered pairs, tables of values or equation) and determine whether it represents a linear relation
  • identify independent and dependent variables
  • determine whether a situation (set of data or table) represents a linear relation and explain why or why not


  • Notes


  • p287 #1-10
FileDescriptionFile size
Download this file (10.6.2.notes.pdf)10.6.2.notes.pdfLinear relations Notes474 kB

10.6.3 Domain and Range

Domain and range tell us all the possible x and y values that are in a relation, although it can be presented in several different ways.

Things you should know after today:

  • definition of domain and range
  • how to write domain and range using:
    • words
    • number lines
    • set notation
    • interval notation (where appropriate)
    • lists (where appropriate)


  • Notes: Set Notation
  • Notes: Domain and Range


  • p301 #1-5, 7, 8, 9, 11

10.6.4 Funcions

Most likely, every formula you have ever used is a function.  For example, finding out how much money you make:  Your hours worked is your input, the earnings is your output, and there is a formula or rule that converts the input into output.

Today, we will see how a function is different from a relation, and how we use notation that makes it more clear what the input and output is.

Things you should know after today:

  • definition of a function
  • the vertical line test
  • how input and output are related to (x,y) coordinates
  • What f(3) means.
  • How to determine f(3) from a graph and from an equation
  • How to determine x if you know f(x) = something



  • p311 #1-8, 10, 11, 14 *12 *15
  • Extra practice #, 2, 4, 7-9

10.6.5 Slope of a Line

Think about how much money you could make if you were working at a job.  You could graph your earnings on the vertical axis, and your earnings on the horizontal axis.  You would have a graph where your total earnings were increasing over time.  What would the graph look like if your hourly rate was higher? What if it was lower?

When you graph a line, you can think about how it looks.  It may be increasing to the right, decreasing to the right, or staying constant/flat.

Today, we will be looking at how the steepness of the line can be assigned a number.


  • Notes: Slope of a Line


  • p325 #1-8, 11, 12, 14 *16 *18

Things you should know after today:

  • the definition of the slope of a line
  • how to determine the slope of a line using a graph
  • how to determine the slope of a line segment between two coordinates using an equation
  • how to draw a line if you are given a coordinate and a slope

10.6.6 Review


  • Watch the video on Youtube that contains two short segments about funcions.  Think about how they are related to what we learned about functions in this chapter:
    • How does the candy dispensing scarecrow relate to our concept of functions and/or relations?
    • The frog is an example of a function.
      • What are some of the terms used in the video that are important for describing functions?
      • What are some of the different ways that the frog function was described?
    • A cell phone is an example of a funcion. When you press the "1" button, you expect it to dial the number 1 only. Find 3 other examples and explain how they are related to our concept of functions.
  • p330 #1-16

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