Foundations in Calculus Fall 2020

Laura, Jul 31, 2020

Foundations in Calculus Review

Table of Contents

  1. Function Review
    1. What Makes a Function Even?
    2. What Makes a Function Odd?
    3. Domain and Range: Quick Quiz Questions and Illustrator
    4. Domain & Range
    5. Interval Notation Illustrator: Single Sets & Conjunctions
    6. Interval Notation: Quiz (Single Sets & Conjunctions)
    7. Inverse functions
  2. Exponent Rules
    1. Exponent Law: Geometric Illustration
    2. Laws of exponent Practice sheet-1
    3. Worksheet-2 for law of exponent
    4. Laws of exponent worksheet-2
    5. Simplify Expressions, More Complicated-Section 4.2-4.3
    6. Simplify Expressions with Exponents, More Diffic-Section 4.2
    7. Fractional Exponents to Radicals
  3. Parent Functions
    1. Linear
    2. Absolute Value Function
    3. Quadratic
    4. Vertex Form Quadratic
    5. Square Root
    6. Exponential 1
    7. Exponential 2
    8. Logarithmic
    9. Cubic
    10. Cube Root
    11. Rational

1.

Function Review

  • 1. What Makes a Function Even?
  • 2. What Makes a Function Odd?
  • 3. Domain and Range: Quick Quiz Questions and Illustrator
  • 4. Domain & Range
  • 5. Interval Notation Illustrator: Single Sets & Conjunctions
  • 6. Interval Notation: Quiz (Single Sets & Conjunctions)
  • 7. Inverse functions

1.1.

What Makes a Function Even?

This app illustrates what it means for a function to be EVEN. Interact with this app for a few minutes. As you do, be sure to move the points around.
Based solely upon your observations (and without looking it up on another tab in your web browser), describe what you think it means for a function to be classified as an [color=#666666][b]EVEN FUNCTION[/b][/color].
– Tim Brzezinski

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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2.

Exponent Rules

  • 1. Exponent Law: Geometric Illustration
  • 2. Laws of exponent Practice sheet-1
  • 3. Worksheet-2 for law of exponent
  • 4. Laws of exponent worksheet-2
  • 5. Simplify Expressions, More Complicated-Section 4.2-4.3
  • 6. Simplify Expressions with Exponents, More Diffic-Section 4.2
  • 7. Fractional Exponents to Radicals

2.1.

Exponent Law: Geometric Illustration

Interact with the applet below for a few minutes. [br][br]Be sure to change the locations of the [b][color=#cc0000]red point[/color][/b] and [b][color=#9900ff]purple point[/color][/b] each time before re-sliding the slider. [br][br](For this illustration, assume lines that appear to be parallel [i]are[/i] parallel.) [br][br]After doing so, please answer the questions that follow.
1.
What can we conclude about the area of the [b][color=#38761d]green rectangle[/color][/b] and the area of the [b][color=#bf9000]yellow rectangle[/color][/b]? Why can we conclude this?
2.
Why does the area of the [b][color=#38761d]green rectangle[/color][/b] never change (despite the transformations we see)?
3.
[b][color=#9900ff]Suppose the length of the purple segment = 2. [/color][/b][br][b][color=#cc0000]Suppose the length of the red segment = 3. [/color][/b][br][br]What would the length of the [b]single-tick segment[/b] be (in terms of [i]a[/i])? [br]What would the length of the [b]double-tick segment[/b] be (in terms of [i]a[/i])?
4.
Given the information in (3), what would the length of the vertical segment (farthest to the right) be? (Express in terms of [i]a[/i]).
5.
Given your response for (1), write a relationship (equation) that contains the expressions you wrote for (3) and (4) above.
6.
In general, what property (law) of exponents does this animation help illustrate? Explain.
Quick (Silent) Demo
– Tim Brzezinski

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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3.

Parent Functions

  • 1. Linear
  • 2. Absolute Value Function
  • 3. Quadratic
  • 4. Vertex Form Quadratic
  • 5. Square Root
  • 6. Exponential 1
  • 7. Exponential 2
  • 8. Logarithmic
  • 9. Cubic
  • 10. Cube Root
  • 11. Rational

3.1.

Linear

– Kevin Tanton

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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Information