Examples for

# Common Core Math: High School Functions: Interpreting Functions

In high school, students study linear, quadratic, polynomial, exponential, logarithmic, rational and trigonometric functions. These functions can be represented with equations, words, graphs, diagrams, sequences or tables. Each time students discover a new type of function, students learn to perform relevant computations for locating key features such as x-intercepts (also called "roots" or "zeros"), y-intercepts, maxima and minima, end behavior, discontinuities, monotonicity, periodicity and more.

### Common Core Standards

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### Function Behavior

With the help of graphs and tables, determine a variety of function behaviors.

#### Find intercepts of functions (CCSS.Math.Content.HSF-IF.B.4):

#### Identify and locate maximum and minimum values of functions (CCSS.Math.Content.HSF-IF.B.4):

#### Describe end behavior of a function (CCSS.Math.Content.HSF-IF.B.4):

#### Determine intervals on which a function has a given behavior (CCSS.Math.Content.HSF-IF.B.4):

#### Find the period of a function (CCSS.Math.Content.HSF-IF.B.4):

### Concept of a Function

Determine key features of functions represented by an equation, graph or table.

#### Determine the domain and range of a function (CCSS.Math.Content.HSF-IF.A.1):

#### Graph a function given its equation (CCSS.Math.Content.HSF-IF.A.1):

#### Evaluate functions (CCSS.Math.Content.HSF-IF.A.2):

#### Express sequences as functions (CCSS.Math.Content.HSF-IF.A.2):

### Computing with Functions

Investigate functions by interpreting and manipulating their equations.

#### Calculate the average rate of change of a function (CCSS.Math.Content.HSF-IF.B.6):

#### Factor and solve quadratic functions (CCSS.Math.Content.HSF-IF.C.8a):

### RELATED EXAMPLES

### Graphing Functions

Use a function's equation and knowledge of key features of a function to sketch its graph.