# Lesson 3Function JunctionPractice Understanding

## Jump Start

Which One Doesn’t Belong?

Use the mathematical features to analyze each relationship and choose which graph doesn’t belong with the others. Explain your reasoning with mathematical vocabulary.

A.
B.
C.
D.
E.
Reason:

## 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.

How do I choose between interval and set builder notation for domains and ranges?

How can I use the relationship between features of functions to help me be more efficient in writing features?

How can I tell if a maximum or minimum is relative or absolute?

## Open Up the Math: Launch, Explore, Discuss

Analyze each function to find the key features. Write each feature using appropriate mathematical notation.

### 1.

The table represents a discrete function defined on the interval from .

Domain:

Range:

Maximum:

Minimum:

Intercept(s):

Interval(s) of increase:

Interval(s) of decrease:

### 2.

Domain:

Range:

Maximum:

Minimum:

Intercept(s):

Interval(s) of increase:

Interval(s) of decrease:

Function (Yes or No):

### 3.

Graph the function, then determine the key features.

Domain:

Range:

Maximum:

Minimum:

Intercept(s):

Interval(s) of increase:

Interval(s) of decrease:

### 4.

Marcus bought a couch on a six-month, interest free payment plan. He pays each week on the loan. Describe the key features of the relationship between the number of weeks and the amount owed on the loan.

Domain:

Range:

Maximum:

Minimum:

Intercept(s):

Interval(s) of increase:

Interval(s) of decrease:

Function (Yes or No):

Discrete/Continuous/Discontinuous:

### 5.

The table represents a continuous function defined on the interval from .

Domain:

Range:

Maximum:

Minimum:

Intercept(s):

Interval(s) of increase:

Interval(s) of decrease:

### 6.

Domain:

Range:

Maximum:

Minimum:

Intercept(s):

Interval(s) of increase:

Interval(s) of decrease:

Function (Yes or No):

Discrete/Continuous/Discontinuous:

### 7.

Describe the key features of the relationship between the number of hours of daylight and the day of the year in your town. Consider January 1 as day , that the longest day of the year is day (about June 22), and the shortest day of the year is day (about December 23). You may need to make some reasonable estimates for the number of daylight hours.

Domain:

Range:

Maximum:

Minimum:

Intercept(s):

Interval(s) of increase:

Interval(s) of decrease:

Function (Yes or No):

Discrete/Continuous/Discontinuous:

### 8.

, when

Graph the function, then determine the key features.

Domain:

Range:

Maximum:

Minimum:

Intercept(s):

Interval(s) of increase:

Interval(s) of decrease:

Draw a graph of a function with the following features:

• Increases on the intervals

• Decreases on the intervals

• Has a relative maximum of

• Has a relative minimum of and another of

• Is continuous

• Contains the point

## Takeaways

Helpful ideas for finding and writing features of functions:

## 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.

## Retrieval

### 1.

Complete the tables.

### 2.

Find the explicit and recursive equations for the table.

### 3.

Find the explicit and recursive equations for the table.