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# Mathematics Functions

## Common Core Standards

### Mathematics: Functions

In Functions, instructional time should focus on developing the concept of a function in terms of three main areas: (1) developing students’ ability to recognize functions and how they can be represented in multiple formats; (2) building functions to model a relationship between two quantities; (3) introducing students to several different types of functions including linear, quadratic, exponential, and trigonometric functions and helping students distinguish when to use a given function type to model a particular situation.
Sophia and Common Core Standards
Our Many Ways to Learn method makes it easy to integrate the new standards into your teaching. By using multiple instructors and teaching styles for each tutorial, we make sure you're reaching your students, so they can reach their goals.
Note: Our Common Core-aligned content is middle and high school-focused. We're continually expanding our library, so stay tuned - more great content coming soon.

## F.IF - Interpreting Functions

##### Analyze functions using different representations
Code
Standard
Concepts
F.IF.7a
Graph linear and quadratic functions and show intercepts, maxima, and minima.
3
F.IF.7b
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
2
F.IF.7c
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
2
F.IF.7d
(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
6
F.IF.7e
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
11
F.IF.8a
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
2
F.IF.8b
Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
3

## F.TF - Trigonometric Functions

##### Extend the domain of trigonometric functions using the unit circle
Code
Standard
Concepts
F.TF.1
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
1
##### Model periodic phenomena with trigonometric functions
Code
Standard
Concepts
F.TF.7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.★
11