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3.3.1: Identifying Key Features of Linear and Exponential Graphs

http://walch.com/wu/CAU3L3S1BikeErrands

The graph below represents Kim’s distance from home one day as she rode her bike to meet friends and to do a couple of errands for her mom before returning home.

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1. Use the graph to describe Kim’s journey.

2. What do the horizontal lines on the graph represent?

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1. Use the graph to describe Kim’s journey.• Answers will vary. One possible response: Kim rode her

bike to her friend’s house. She stayed at her friend’s house for a while. Then she left her friend’s house and rode to a store, which is even farther away from her house. She stayed at the store for a short time and bought a couple of items. Kim then headed back toward her house, stopping once more to take a picture of a beautiful statue along the way. She then biked the rest of the way back home.

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2. What do the horizontal lines represent in the graph? • The horizontal lines represent times when Kim stayed

at one location. Her distance from home did not change, but time continued to pass.

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Lesson 3.4 – Characteristics of Linear FunctionsConcepts: Characteristics of Linear Functions

EQ: What are the key features of a linear function? (Standard F.IF.7)

Vocabulary:Rate of changeDomain/Rangex and y interceptsIntervals of Increasing/DecreasingExtrema (Minimum/Maximum)

Key Features of Linear Functions

Domain & Range

Intercepts (x & y)

Increasing/Decreasing

Extrema (Minimum/Maximum)

Rate of Change Back

Intervals

Identifying Key Features of a Linear Function

Domain and Range:Domain: all possible input valuesRange: all possible output values

Example: Domain: 1, 2, 3 Range: 4, 5, 6


Intercepts:X-intercept: The place on the x-axis

where the graph crosses the axis.-Ordered pair: (x, 0)


Intercepts:X-intercept: The place on the x-axis

where the graph crosses the axis.-Ordered pair: (x, 0)

Example 2: y = x + 20 = x +2-2 = x

x-intercept: (-2, 0)


Intercepts:y-intercept: The place on the y-axis

where the graph crosses the axis-Ordered pair: (0, y)


Intercepts:y-intercept: The place on the y-axis

where the graph crosses the axis-Ordered pair: (0, y)

Example 2: y = x + 2y = 0 +2y = 2

y-intercept: (0, 2)


Increasing or Decreasing????

Increasing: A function is said to increase if while the values for x increase as well as the values for y increase. (Both x and y increase)


Increasing or Decreasing????

Decreasing: A function is said to decrease if one of the variables increases while the other variable decreases. (Ex: x increases, but y decreases)


Intervals:An interval is a continuous series of values. (Continuous means “having no breaks”.)We use two different types of notation for intervals: 1. Brackets ( ) or [ ]

Ex: [0, 3] and 0< x < 3 both mean all values between 0 and 3 inclusive

2. inequality symbols ≤, ≥, <, >Non-inclusive Inclusive


Intervals:A function is positive when its graph is above

the x-axis.A function is negative when its graph is

below the x-axis.

Identifying Key Features of a Graph

The function is positive when x > ?

When x ≥ 4! Or [4, ∞)

Identifying Key Features of a Graph

The function is negative when x < ?

When x < 4! Or (-∞, 4)


Extrema:A relative minimum is the point that is the lowest,

or the y-value that is the least for a particular interval of a function.

A relative maximum is the point that is the highest, or the y-value that is the greatest for a particular interval of a function.

Linear functions will only have a relative minimum or maximum if the domain is restricted.


Identifying Rate of Change

Rate of Change:Rate of change or Slope is found by using the

following equation:

Or by reading the rise over the run from a graph.

12

12

xxyym

Identifying Rate of Change

Identify two points on the line.(0, 2) and (5, 1)Use the formula:

51

0521

12

12

xxyym

Example 1:

Guided PracticeExample 1• A taxi company in Atlanta

charges $2.75 per ride plus $1.50 for every mile driven. Determine the key features of this function.

Identify the following:1. Type of function2. Domain and Range3. Y-intercept4. Intervals of Increasing

or Decreasing 5. Extrema6. Rate of Change

Example 2:

A gear on a machine turns at a rate of 3 revolutions per second. Identify the key features of the graph of this function.



Example 3:

An online company charges $5.00 a month plus $2.00 for each movie you decide to download.

Identify the following:1. Type of function2. Domain and Range3. Y-intercept4. Intervals of Increasing or

Decreasing 5. Extrema6. Rate of Change

Example 4:A ringtone company charges $15 a month plus $2 for each ringtone downloaded. Create a graph and then determine the key features of this function.



You Try 1The starting balance of Adam’s savings account is $575. Each

month, Adam deposits $60.00. Adam wants to keep track of his deposits so he creates the following equation: f(x) = 60x + 575, where x = number of months.



You Try 2The cost of an air conditioner is $110. The cost to run the air conditioner is $0.35 per minute. The table below represents this relationship. Graph and identify the key features of this function.



3-2-1 Summary

Name 3 new features you learned about today.

Name 2 features you already knew about.

Name 1 feature you still need to practice identifying.

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