CCSS High School: Functions (Interpreting Functions)
1. HSF.IF.A.1
1. Functions: Input and Output (I)
2. Functions: Input & Output (II)
3. Functions: Input & Output (3)
4. Functions: Input & Output (4)
5. Functions: Input & Output (III)
6. Function Or Not?
2. HSF.IF.A.2
1. Evaluating Functions Using Graphs (Quiz)
2. Evaluating Functions Algebraically
3. Quiz: Function Operations (1)
4. Composition of Functions: Algebraic (Quiz)
5. Quiz: Composition of Functions (Graph & Table)
6. Composition of Functions: Graphical (Quiz) - V1
3. HSF.IF.A.3
1. Sequences (Dynamic Illustrator)
4. HSF.IF.B.4
1. Function Behavior
2. Quick Intercepts Illustrator
3. Relative Extrema Illustrator
4. Polynomial End Behavior (Dance...)
5. What Makes a Function Even?
6. Animation 143
7. What Makes a Function Odd?
8. Animation 144
9. Odd Functions (Another Look)
10. Odd Functions: Another Look (Take 2)!
11. Periodic Function Action!
12. Animation 189
13. Sine & Cosine Period Action (1)!
14. Animation 190
15. Animation 191
16. Sine & Cosine Period Action (1)!
17. Sine & Cosine Period Action (2)!
18. Tangent Period Action (1)!
19. Animation 192
20. Tangent Period Action (2)!
21. Dolbear's Law
22. Half-Life Function
5. HSF.IF.B.5
1. Domain & Range Illustrator
2. Animation 95
3. Animation 93
6. HSF.IF.B.6
1. Average Rate of Change of a Function: Dynamic Illustration
2. The Difference Quotient (Illustrated)
3. Quiz: Average Rate of Change of a Function (1)
4. Quiz: Average Rate of Change (2)
5. Quiz: Average Rate of Change of a Function (3)
7. HSF.IF.C.7, 7.A, 7.B, 7.C, 7.D, 7.E
1. Sketching Graph Models
2. Equation of a Line: Dynamic Illustrator
3. Quadratic Function
4. Absolute Value Function
5. Square Root Function
6. Cube Root Function
7. Exponential Functions: Graphs
8. Exponential Functions (Graph & Equation Anatomy)
9. Logarithmic Functions: Graphs
10. Logarithmic Functions (Graph & Equation Anatomy)
11. Quiz: Dividing Polynomial Expressions
12. Graphing Sine & Cosine Functions (II)
13. Graphing Sine & Cosine Functions (I)
14. Graph y = a sin(x) + d (Quiz)
15. Graph y = a cos(x) + d (Quiz)
16. Rational Function Grapher
8. HSF.IF.C.8, 8.A, 8.B, C.9
1. Completing the Square (1)
2. Completing the Square (2)
3. Completing the Square (3)
4. Quiz: Completing the Square (1)
5. Quiz: Completing the Square (2)
6. Exponential Growth vs. Decay (Intro)
7. Quiz: Writing Exponential Growth & Decay Functions
9. Links to Other CCSS High School: Functions Resources
1. Functions Resources
10. *Additional: Links to CCSS High School: Geometry Resources
1. Geometry Resources

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CCSS High School: Functions (Interpreting Functions)

Tim Brzezinski, JohnCMorris, Oct 26, 2017

This GeoGebra Book contains discovery-based learning activities, investigations, and meaningful remediation worksheets that were designed to help enhance students' learning of concepts related to interpreting functions.

HSF.IF.A.1
1. Functions: Input and Output (I)
2. Functions: Input & Output (II)
3. Functions: Input & Output (3)
4. Functions: Input & Output (4)
5. Functions: Input & Output (III)
6. Function Or Not?
HSF.IF.A.2
1. Evaluating Functions Using Graphs (Quiz)
2. Evaluating Functions Algebraically
3. Quiz: Function Operations (1)
4. Composition of Functions: Algebraic (Quiz)
5. Quiz: Composition of Functions (Graph & Table)
6. Composition of Functions: Graphical (Quiz) - V1
HSF.IF.A.3
1. Sequences (Dynamic Illustrator)
HSF.IF.B.4
1. Function Behavior
2. Quick Intercepts Illustrator
3. Relative Extrema Illustrator
4. Polynomial End Behavior (Dance...)
5. What Makes a Function Even?
6. Animation 143
7. What Makes a Function Odd?
8. Animation 144
9. Odd Functions (Another Look)
10. Odd Functions: Another Look (Take 2)!
11. Periodic Function Action!
12. Animation 189
13. Sine & Cosine Period Action (1)!
14. Animation 190
15. Animation 191
16. Sine & Cosine Period Action (1)!
17. Sine & Cosine Period Action (2)!
18. Tangent Period Action (1)!
19. Animation 192
20. Tangent Period Action (2)!
21. Dolbear's Law
22. Half-Life Function
HSF.IF.B.5
1. Domain & Range Illustrator
2. Animation 95
3. Animation 93
HSF.IF.B.6
1. Average Rate of Change of a Function: Dynamic Illustration
2. The Difference Quotient (Illustrated)
3. Quiz: Average Rate of Change of a Function (1)
4. Quiz: Average Rate of Change (2)
5. Quiz: Average Rate of Change of a Function (3)
HSF.IF.C.7, 7.A, 7.B, 7.C, 7.D, 7.E
1. Sketching Graph Models
2. Equation of a Line: Dynamic Illustrator
3. Quadratic Function
4. Absolute Value Function
5. Square Root Function
6. Cube Root Function
7. Exponential Functions: Graphs
8. Exponential Functions (Graph & Equation Anatomy)
9. Logarithmic Functions: Graphs
10. Logarithmic Functions (Graph & Equation Anatomy)
11. Quiz: Dividing Polynomial Expressions
12. Graphing Sine & Cosine Functions (II)
13. Graphing Sine & Cosine Functions (I)
14. Graph y = a sin(x) + d (Quiz)
15. Graph y = a cos(x) + d (Quiz)
16. Rational Function Grapher
HSF.IF.C.8, 8.A, 8.B, C.9
1. Completing the Square (1)
2. Completing the Square (2)
3. Completing the Square (3)
4. Quiz: Completing the Square (1)
5. Quiz: Completing the Square (2)
6. Exponential Growth vs. Decay (Intro)
7. Quiz: Writing Exponential Growth & Decay Functions
Links to Other CCSS High School: Functions Resources
1. Functions Resources
*Additional: Links to CCSS High School: Geometry Resources
1. Geometry Resources

Information

1.

HSF.IF.A.1

1. Functions: Input and Output (I)
2. Functions: Input & Output (II)
3. Functions: Input & Output (3)
4. Functions: Input & Output (4)
5. Functions: Input & Output (III)
6. Function Or Not?

1.1.

Functions: Input and Output (I)

– Tim Brzezinski

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

2.

HSF.IF.A.2

1. Evaluating Functions Using Graphs (Quiz)
2. Evaluating Functions Algebraically
3. Quiz: Function Operations (1)
4. Composition of Functions: Algebraic (Quiz)
5. Quiz: Composition of Functions (Graph & Table)
6. Composition of Functions: Graphical (Quiz) - V1

2.1.

Evaluating Functions Using Graphs (Quiz)

– 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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3.

HSF.IF.A.3

1. Sequences (Dynamic Illustrator)

3.1.

Sequences (Dynamic Illustrator)

A sequence is a function whose domain is the set of positive (or sometimes, nonnegative) integers. Recall the domain of a function is the set of all values that can be inputted into the function. The following applet dynamically and graphically illustrates the meaning of a sequence. Feel free to re-author the explicit formula for this sequence in the upper left-hand corner.

– Tim Brzezinski

4.

HSF.IF.B.4

1. Function Behavior
2. Quick Intercepts Illustrator
3. Relative Extrema Illustrator
4. Polynomial End Behavior (Dance...)
5. What Makes a Function Even?
6. Animation 143
7. What Makes a Function Odd?
8. Animation 144
9. Odd Functions (Another Look)
10. Odd Functions: Another Look (Take 2)!
11. Periodic Function Action!
12. Animation 189
13. Sine & Cosine Period Action (1)!
14. Animation 190
15. Animation 191
16. Sine & Cosine Period Action (1)!
17. Sine & Cosine Period Action (2)!
18. Tangent Period Action (1)!
19. Animation 192
20. Tangent Period Action (2)!
21. Dolbear's Law
22. Half-Life Function

4.1.

Function Behavior

Feel free to start by putting the 2 white points anywhere you'd like. Then slide the slider. Please answer the questions that follow.

1.

How would you describe the pieces of the function that are BLUE? Explain.

Font sizeFont size

Very smallSmallNormalBigVery big

Bold [ctrl+b]

Italic [ctrl+i]

Underline [ctrl+u]

Strike

Superscript

Subscript



Font color

Auto

Justify

Align left

Align right

Align center

• Unordered list

1. Ordered list

Link [ctrl+shift+2]

Quote [ctrl+shift+3]

[code]Code [ctrl+shift+4]

Insert table

Remove Format

Insert image [ctrl+shift+1]

Insert icons of GeoGebra tools

[bbcode]

Text tools

Insert Math

2.

How would you describe the pieces of the function that are RED? Explain.

Font sizeFont size

Very smallSmallNormalBigVery big

Bold [ctrl+b]

Italic [ctrl+i]

Underline [ctrl+u]

Strike

Superscript

Subscript



Font color

Auto

Justify

Align left

Align right

Align center

• Unordered list

1. Ordered list

Link [ctrl+shift+2]

Quote [ctrl+shift+3]

[code]Code [ctrl+shift+4]

Insert table

Remove Format

Insert image [ctrl+shift+1]

Insert icons of GeoGebra tools

[bbcode]

Text tools

Insert Math

3.

How would you describe the pieces of the function that are BLACK? Explain.

Font sizeFont size

Very smallSmallNormalBigVery big

Bold [ctrl+b]

Italic [ctrl+i]

Underline [ctrl+u]

Strike

Superscript

Subscript



Font color

Auto

Justify

Align left

Align right

Align center

• Unordered list

1. Ordered list

Link [ctrl+shift+2]

Quote [ctrl+shift+3]

[code]Code [ctrl+shift+4]

Insert table

Remove Format

Insert image [ctrl+shift+1]

Insert icons of GeoGebra tools

[bbcode]

Text tools

Insert Math

Quick (Silent) Demo

– Tim Brzezinski

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

4.7.

–

4.8.

–

4.9.

–

4.10.

–

4.11.

–

4.12.

–

4.13.

–

4.14.

–

4.15.

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4.16.

–

4.17.

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4.18.

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4.19.

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4.20.

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4.21.

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4.22.

–

5.

HSF.IF.B.5

1. Domain & Range Illustrator
2. Animation 95
3. Animation 93

5.1.

Domain & Range Illustrator

– Tim Brzezinski

5.2.

–

5.3.

–

6.

HSF.IF.B.6

1. Average Rate of Change of a Function: Dynamic Illustration
2. The Difference Quotient (Illustrated)
3. Quiz: Average Rate of Change of a Function (1)
4. Quiz: Average Rate of Change (2)
5. Quiz: Average Rate of Change of a Function (3)

6.1.

Average Rate of Change of a Function: Dynamic Illustration

The average rate of change of a continuous function f from input value x = a to input value x = b is given by

. The applet below provides a dynamic visual interpretation of this expression. Interact with this applet for a few minutes. You can input different functions in the input box in the upper right-hand corner. You can also adjust the input values a and b using the sliders or their respective input boxes.

– Tim Brzezinski

6.2.

–

6.3.

–

6.4.

–

6.5.

–

7.

HSF.IF.C.7, 7.A, 7.B, 7.C, 7.D, 7.E

1. Sketching Graph Models
2. Equation of a Line: Dynamic Illustrator
3. Quadratic Function
4. Absolute Value Function
5. Square Root Function
6. Cube Root Function
7. Exponential Functions: Graphs
8. Exponential Functions (Graph & Equation Anatomy)
9. Logarithmic Functions: Graphs
10. Logarithmic Functions (Graph & Equation Anatomy)
11. Quiz: Dividing Polynomial Expressions
12. Graphing Sine & Cosine Functions (II)
13. Graphing Sine & Cosine Functions (I)
14. Graph y = a sin(x) + d (Quiz)
15. Graph y = a cos(x) + d (Quiz)
16. Rational Function Grapher

7.1.

Sketching Graph Models

Students: Use these templates to draw general sketches of each scenario listed on the scenarios page given to you at the beginning of class. Then submit either via our GeoGebra Group or Google Classroom.