# Unit 3Features of Functions

## Lesson 1

### Learning Focus

Graph a function to model a situation.

Interpret and identify key features of the graph.

### Lesson Summary

In this lesson, we created graphs to model a story context. We learned the mathematical words to describe the key features of functions. These key features are used to analyze and compare functions.

## Lesson 2

### Learning Focus

Identify key features of functions.

Use key features of functions to analyze tables and graphs.

### Lesson Summary

In the lesson we learned how to find features of functions in a table and clarified what each feature describes. We learned to use interval notation to write domains, ranges, and intervals of increase and decrease for continuous functions.

## Lesson 3

### Learning Focus

Become efficient in identifying key features of functions in various representations.

Describe domain, range, and intervals of increase and decrease using appropriate notation.

### Lesson Summary

In this lesson, we worked on becoming fluent, flexible, and accurate in identifying and writing the key features of functions. We learned that domain and range can both be written as lists in set builder notation. We learned to identify features from context and to use graphs to help visualize the features.

## Lesson 4

### Learning Focus

Interpret the graphs and equations of functions.

Write equations for the graph of functions.

Combine two linear functions.

### Lesson Summary

In this lesson we wrote the equation of two functions given graphically and with a story context. We connected the domain and range to the context and the graph. We deepened our understanding of function notation, learning to interpret the notation for graphs, tables, and equations. We learned that functions can be added together both graphically and algebraically.

## Lesson 5

### Learning Focus

Interpret function notation to match a function with its features.

### Lesson Summary

In this lesson we interpreted function notation to match features with functions. We learned common phrases that can be used to “translate” function notation depending on the context. For instance, can be interpreted as the height of the graph at is or that when is substituted into , the output is .

## Lesson 6

### Learning Focus

Write and graph equations of functions.

Compare the graphs of related functions.

### Lesson Summary

In this lesson, we learned that adding or subtracting a number to a function results in a vertical translation of the graph. In a vertical translation, functions do not change their shape, they are simply shifted up or down.