HSF-BF.B.3

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- HSF-BF.B.3Identify 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.
- HSF-BF.B.4Find inverse functions.
- HSF-BF.B.5(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

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## 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)

Big Idea:

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

Standards:

Favorites
(38)

Resources
(19)

Reflections
(2)

### Can the Dog Reach the Bone? Determine whether a Point Lies within a Circle

12th Grade Math »
Unit: Circles

12th Grade Math »
Unit: Circles

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.

Standards:

Favorites
(10)

Resources
(14)

Reflections
(1)

### Transformation of Polynomial Functions

Algebra II »
Unit: Polynomial Functions

Algebra II »
Unit: Polynomial Functions

Big Idea:

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

Standards:

Resources
(30)

Reflections
(2)

### 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

Big Idea:

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

Standards:

Favorites
(1)

Resources
(7)

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.

Standards:

Resources
(13)

Reflections
(1)

### End of Unit Differentiated Problem Set

Algebra II »
Unit: Exponential and Logarithmic Functions

Algebra II »
Unit: Exponential and Logarithmic Functions

Big Idea:

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

Standards:

Favorites
(1)

Resources
(14)

### Shifting Exponential Functions

12th Grade Math »
Unit: Exponential Functions and Equations

12th Grade Math »
Unit: Exponential Functions and Equations

Big Idea:

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

Standards:

Favorites
(6)

Resources
(19)

Reflections
(1)

Big Idea:

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

Standards:

Favorites
(8)

Resources
(13)

Reflections
(1)

### Stretching Exponential Functions (and your mind)

12th Grade Math »
Unit: Exponential Functions and Equations

12th Grade Math »
Unit: Exponential Functions and Equations

Big Idea:

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

Standards:

Favorites
(2)

Resources
(19)

### Finding Vertices of Parabolas

12th Grade Math »
Unit: More Abstract Work with Quadratic Functions

12th Grade Math »
Unit: More Abstract Work with Quadratic Functions

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?

Standards:

Favorites
(4)

Resources
(13)

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.

Standards:

Favorites
(2)

Resources
(10)

### 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

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.

Standards:

Resources
(10)

Reflections
(1)

### 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

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.

Standards:

Favorites
(1)

Resources
(12)

### Profit Maximization

12th Grade Math »
Unit: More Abstract Work with Quadratic Functions

12th Grade Math »
Unit: More Abstract Work with Quadratic Functions

Big Idea:

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

Standards:

Resources
(12)

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