Lesson 3 Function Junction Practice 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.
The graph begins at (-5, 5), descends in a line to (0, 0), then ascends in a line to (5, 5). The graph looks like a V. x–5–5–5555y–5–5–5555000
B.
The graph begins at (-6, -8), ascends in a line to (-3, -5), where it ends with a closed dot. Beginning at (-3, -2) with an open dot, it ascends in a continuous line to (6,6), where it ends. x–5–5–5555y–5–5–5555000
C.
The graph is a curve. It begins at (9, 4), curves to the left until it reaches the origin, then curves to the right, until it reaches (9, -4), where it ends. It is symmetric x555y–5–5–5000
D.
Six points are plotted in a downward curve. (-1, 8),(0, 4)(1, 2)(2, 1)(3,1 over 2)and (4, 1 over 4) . x555y555101010000
E.
The graph begins at (-3,- 5), ascends in a curve to (0, 5), then descends in a curve to (3, -5). The graph is symmetric with the y-axis. x–5–5–5555y–5–5–5555000
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.

a curved line of a coordinate plane x–5–5–5555101010y555000

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:

a blank 17 by 17 grid

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.

The graph begins at 0,-10 with a closed dot. It descends in a smooth curve to (6, 4) with a closed dot. It begins at (6, 7) with an open dot, ascending up in a smooth curve to about (8, 9), then descending in a smooth curve to about (18, -18.5), where it turns upward in a smooth curve to 21, 0. It ends at a closed dot. x555101010151515202020y555101010000

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:

a blank 17 by 17 grid

Ready for More?

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

a blank 17 by 17 grid

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.

a.

b.

2.

Find the explicit and recursive equations for the table.

3.

Find the explicit and recursive equations for the table.