Linear vs. Quadratic vs. Exponential

Introduction

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Hello, and welcome to class! A very important part of mathematics is the ability to be curious and explore that curiosity. Today we are going to explore different sources to learn about the similarities and differences between linear, quadratic, and exponential functions. We are going to start by learning about each one individually, then we are going to compare the three function types. The goal of this lesson is to learn key terms so that you can correctly identify the function type from a table, a graph, or an equation. All three functions have different techniques for solving, so it is crucial that we can correctly identify the function type before we start working!

Task

During this WebQuest, you are going to be using different websites to learn a general overview about the three types of functions. You will write down and define any important terms (specific terms will be given in process). For each function type, you are going to first graph the function using an online graphing calculator. When you graph the functions please pay attention to the shape of each type. After you have explored each function using the graphing tool, you will then be linked to a video about that function and given terms to define. After taking notes on all three functions, you will then complete the Venn diagram to prove what you have learned. Your main goal is to understand the key similarities and differences between the three different functions!

Unit13

Process

Linear Functions

  1. Use this link to get to the Desmos graphing calculator. https://www.desmos.com/calculator *Please see attached video if you have any trouble graphing with Desmos. https://www.youtube.com/watch?v=6SpIlYzIWbo*
  2. In the first input box, type in "y = x" then click and drag the mouse to explore the graph.
  3. Click on the second input box and type in "y = -x" then click and drag the mouse to explore the graph.
  4. After you have looked at the graphs please watch this video about linear functions. https://www.youtube.com/watch?v=MXV65i9g1Xg
  5. On a separate sheet of paper, define the following terms as you watch the video.
    1. Origin
    2. Slope
    3. Y - axis
    4. X  - axis
    5. Y - Intercept

Quadratic Functions

  1. Use this link to get to the Desmos graphing calculator. https://www.desmos.com/calculator *Please see attached video if you have any trouble graphing with Desmos. https://www.youtube.com/watch?v=6SpIlYzIWbo*
  2. In the first input box, type in "y = x^2" then click and drag the mouse to explore the graph. 
  3. Click on the second input box and type in "y = -x^2" then click and drag the mouse to explore the graph.
  4. After you have looked at the graphs please watch this video about quadratic functions. https://www.youtube.com/watch?v=xSpFz8JDbZk
  5. On the same sheet of paper where you wrote your linear terms, define the following terms as you watch the video.
    1. Quadratic Function (in video it's called Quadratic Relation)
    2. Parabola
    3. Vertex
    4. Minimum
    5. Maximum
    6. Axis of Symmetry

Exponential Functions

  1. Use this link to get to the Desmos graphing calculator. https://www.desmos.com/calculator *Please see attached video if you have any trouble graphing with Desmos. https://www.youtube.com/watch?v=6SpIlYzIWbo*
  2. In the first input box, type in "y = 2^x" then click and drag the mouse to explore the graph. 
  3. Click on the second input box and type in "y = -2^x" then click and drag the mouse to explore the graph.
  4. After you have looked at the graphs please watch this video about exponential functions. https://www.youtube.com/watch?v=tAaDItpC8OI&t=14s
  5. On the same sheet of paper where you wrote your linear and quadratic terms, define the following terms as you watch the video.
    1. Base
    2. Inital Value
    3. Common Ratio

Venn Diagram

  1. Use this link to get to SmartDraw.com: https://www.smartdraw.com/venn-diagram/venn-diagram-software.htm?id=382478&gad_source=1&gad_campaignid=35194876&gbraid=0AAAAAD_wclbZNWz1vIObTJz8o7BXEtfY-&gclid=CjwKCAjwxb7RBhA5EiwAQ-AAdAHTOUPdjywzyiUaBJ88KLLD_PtMw5Cogs_2k-9DBRdtW9CKRLNQ_hoCcxkQAvD_BwE
  2. Click on the yellow button that says "Create your Venn Diagram"
  3. On this page, you will see many different templates. Please select the one that says "Venn Diagram" and looks like three circles.
  4. You will see a page that has three circles (one red, one blue, one green).
    1. Label the red circle "Linear"
    2. Label the blue circle "Quadratic"
    3. Label the green circle "Exponential"
  5. Use the terms you have defined and think about which function(s) each term could apply to. For example, all three types of functions can have a Y-Intercept. Therefore, you would put "Y-intercept" in the intersection of all three circles. Complete this process for all defined terms. 

Evaluation

The following rubric will be used to grade this WebQuest. 

Grading Areas 5 10 15 20 Points Earned by Student
Linear Functions Terms Student has failed to accurately define at least 3 terms. Student accurately defined at least 3 terms. Student accurately defined at least 4 terms. Student accurately defined all terms.  
Quadratic Functions Terms Student has failed to accurately define at least 3 terms. Student accurately defined at least 3 terms. Student accurately defined at least 4-5 terms. Student accurately defined all terms.  
Exponential Functions Terms Student attempted to define, but did not correctly to define any terms. Student accurately defined 1 term. Student accurately defined 2 terms. Student accurately defined all terms.  
Venn Diagram Student created a venn diagram but failed to correctly categorize any terms.  Student created a venn diagram and correctly categorized at least 5 terms.  Student created a venn diagram and correctly categorized at least 10 terms.  Student created a venn diagram and correctly categorized all terms.   
Total Points:          

 

 

Conclusion

Today you have researched the three main types of functions that we will talk about in Algebra 1. Over the next few weeks, we will cover each type in more detail. The purpose of this quest was for you to preview the topics we will cover. As we go into more detail, you will be able to rely on the base knowledge that you learned today. Thank you for your hard work, and I hope you look forward to learning more about these important functions!

 

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Credits