Functions

Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range

Use and interpret function notation and evaluate functions for inputs

Recognize that sequences are functions
Lesson SetsFIF.3
1. Represent an arithmetic sequence as an explicit ruleFIF.3

2. Represent explicit rules as linear functionsFIF.3

3. Use explicit rules to write sequences recursivelyFIF.3

4. Explore the Fibonacci sequence as an example of a recursive sequenceFIF.3

5. Represent a geometric sequence as an explicit ruleFIF.3

6. Represent an explicit rule as an exponential functionFIF.3

7. Write a geometric sequence recursivelyFIF.3


Relate the domain of a function to its graph and to the quantitative relationship it describes

Graph linear functions and show intercepts

Graph quadratic functions and show intercepts
Lesson SetsFIF.7a
1. Identify features of a quadratic equationFIF.7a

2. Graph a quadratic function using the zeros and vertexFIF.7a

3. Graph quadratic functions using the vertex and another pointFIF.7a

4. Write a quadratic equation in vertex form by completing the squareFIF.7a

5. Graph quadratic equations using vertex form and the leading coeffic...FIF.7a

6. Write a quadratic equation using points on the parabolaFIF.7a


Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions

Graph exponential and logarithmic functions

Show and interpret zeros, extreme values, and symmetry of the graph by factoring and completing the square
Lesson SetsFIF.8a
1. Find zeros, extreme values and lines of symmetry using different formsFIF.8a

2. Find zeros and lines of symmetry using factored formFIF.8a

3. Find zeros and lines of symmetry using factored form when a > 1FIF.8a

4. Find extreme values and lines of symmetry using vertex formFIF.8a

5. Find extreme values and lines of symmetry using vertex form when a>1FIF.8a

6. Find zeros and extreme values using factored and vertex formFIF.8a


Use the properties of exponents to interpret expressions for exponential functions

Distinguish between linear and exponential functions
Lesson SetsFLE.1a
1. Identify linear functions linking equal differences to equal intervalsFLE.1a

2. Graph an exponential functionFLE.1a

3. Understand the rate of change in exponential growth functionsFLE.1a

4. Distinguish between linear and exponential functions by examining i...FLE.1a

5. Distinguish between linear and exponential functions using tablesFLE.1a


Recognize when one quantity changes at a constant rate per unit

Recognize when one quantity grows or decays by a constant percent rate per unit interval of another

Express solutions to exponential models as logarithms; evaluate using technology

Understand radian measure of an angle

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers
Lesson SetsFTF.2
1. Understand the wrapping function using the unit circleFTF.2

2. Find trigonometric values for angles using reference trianglesFTF.2

3. Understand quandrantal angles by examining x and y values near themFTF.2

4. Graph f(x)=sinx and g(x)=cosx using the unit circleFTF.2

5. Graph trigonometric functions using a graphing calculatorFTF.2


Choose trigonometric functions to model periodic phenomena
Lesson SetsFTF.5
1. Graph sinusoidal functions by plotting pointsFTF.5

2. Stretch sinusoidal functions horizontally and verticallyFTF.5

3. Transform sinusoidal functions by shifting their graphs horizontall...FTF.5

4. Graph tangent, secant, cosecant, and cotangent by drawing on sine a...FTF.5

5. Model periodic phenomena using trigonometric functionsFTF.5


Prove the Pythagorean identity sin2(?) + cos2(?) = 1
Lesson SetsFTF.8
1. Derive the Pythagorean identity using similar trianglesFTF.8

2. Prove the Pythagorean Identity using a triangle inside the unit circleFTF.8

3. Prove the Pythagorean Identity using the unit circleFTF.8

4. Find trigonometric values using the Pythagorean IdentityFTF.8

5. Derive new Pythagorean identitiesFTF.8
