HSF-BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

 
123 Lesson(s)
   

What is Algebra?

Algebra II » Unit: Modeling with Algebra
Algebra II » Unit: Modeling with Algebra
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

Algebra is built on axioms and definitions and relies on proofs just as much as geometry.

 
Favorites (35)
 
Resources (19)
 
Reflections (2)
al khwarizmi stamp
   

Transformation of Functions Day 1

Algebra I » Unit: Functions
Algebra I » Unit: Functions
James Bialasik
Amherst, NY
Environment: Suburban
 
Big Idea:

Students will use structure and patterns to determine the "rules" for translating functions.

 
Favorites (14)
 
Resources (19)
 
Reflections (1)
transformation functions image
   

Transformation of Polynomial Functions

Algebra II » Unit: Polynomial Functions
Algebra II » Unit: Polynomial Functions
Amelia Jamison
Caldwell, ID
Environment: Rural
 
Big Idea:

Models support conceptual understanding of function transformations. From cube to cubic!

 
Resources (30)
 
Reflections (2)
image transformation of polynomial functions
   
12th Grade Math » Unit: Circles
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

Will the dog be able to reach its bone? Students apply the definition of a circle, along with a method for determining whether or not a point lies on a circle.

 
Favorites (8)
 
Resources (14)
 
Reflections (1)
screenshot 2014 05 13 15 24 12
   

Quadratic Functions Review and Portfolio

12th Grade Math » Unit: More Abstract Work with Quadratic Functions
12th Grade Math » Unit: More Abstract Work with Quadratic Functions
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

What are the key ideas and skills of this unit? What do you most need to review or understand better?

 
Favorites (1)
 
Resources (7)
gravity parabola
   

End of Unit Differentiated Problem Set

Algebra II » Unit: Exponential and Logarithmic Functions
Algebra II » Unit: Exponential and Logarithmic Functions
Jarod Hammel
Huntington, IN
Environment: Suburban
 
Big Idea:

This lesson allows the students to apply their mathematical knowledge in a real context.

 
Favorites (1)
 
Resources (14)
richterscalepicture
   

Standard Form of Circle Equations

12th Grade Math » Unit: Circles
12th Grade Math » Unit: Circles
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

How can I tell if this weird-looking equation will make a circle when I graph it? Students discover how to apply previous knowledge about completing the square to a new problem.

 
Resources (13)
 
Reflections (1)
concentric circles
   

Shifting Exponential Functions

12th Grade Math » Unit: Exponential Functions and Equations
12th Grade Math » Unit: Exponential Functions and Equations
Tiffany Dawdy
Phoenix, AZ
Environment: Urban
 
Big Idea:

Building on yesterday’s idea, key features of exponential graphs, students see how parameter changes of the function can change these features.

 
Favorites (5)
 
Resources (19)
 
Reflections (1)
shifting exponential functions summary image
   

Transformations "How To" Guide

Algebra I » Unit: Functions
Algebra I » Unit: Functions
James Bialasik
Amherst, NY
Environment: Suburban
 
Big Idea:

Students will be producing a "how to" guide for horizontal and vertical transformations of functions.

 
Favorites (7)
 
Resources (13)
 
Reflections (1)
transformations how to image
   

Stretching Exponential Functions (and your mind)

12th Grade Math » Unit: Exponential Functions and Equations
12th Grade Math » Unit: Exponential Functions and Equations
Tiffany Dawdy
Phoenix, AZ
Environment: Urban
 
Big Idea:

Students’ algebraic skills are reinforced as they discover that some different transformations are actually equivalent.

 
Favorites (2)
 
Resources (19)
mind stretch
   

Finding Vertices of Parabolas

12th Grade Math » Unit: More Abstract Work with Quadratic Functions
12th Grade Math » Unit: More Abstract Work with Quadratic Functions
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

Why is finding the vertex of a parabola useful? How can you find the vertex when the function rule is written different ways?

 
Favorites (4)
 
Resources (13)
graph analysis
   

Circle Lattice Points

12th Grade Math » Unit: Circles
12th Grade Math » Unit: Circles
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

Instead of telling students the equation for a circle, developing it themselves enables students to make the connection between circles and the Pythagorean Theorem.

 
Favorites (2)
 
Resources (10)
screenshot 2014 05 13 15 34 04
   

Further Exploration of Distance Functions

12th Grade Math » Unit: Absolute Value Functions and More Piecewise Functions
12th Grade Math » Unit: Absolute Value Functions and More Piecewise Functions
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

Are there function rules to fit these relationships? Students apply prior knowledge to a new problem and find functions to fit their data. The optional use of technology allows them to check models on their own.

 
Resources (10)
 
Reflections (1)
screen shot 2013 09 05 at 4 40 36 pm
   

More 4-Column Data Tables

12th Grade Math » Unit: More Abstract Work with Quadratic Functions
12th Grade Math » Unit: More Abstract Work with Quadratic Functions
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

What happens when we remove the two middle columns? Students develop a method to solve problems with even less information given than the day before.

 
Resources (12)
filling in data tables 2 ways
   

Profit Maximization

12th Grade Math » Unit: More Abstract Work with Quadratic Functions
12th Grade Math » Unit: More Abstract Work with Quadratic Functions
Hilary Yamtich
Oakland, CA
Environment: Urban
 
Big Idea:

What happens to the number of customers as you increase the price of the item? How does this affect your profit?

 
Resources (12)
profit maximization student work
Common Core Math
 
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