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Check it out!
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3.3.1: Identifying Key Features of Linear and Exponential Graphs
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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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3.3.1: Identifying Key Features of Linear and Exponential Graphs
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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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3.3.1: Identifying Key Features of Linear and Exponential Graphs
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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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3.3.1: Identifying Key Features of Linear and Exponential Graphs
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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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3.3.1: Identifying Key Features of Linear and Exponential Graphs
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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)
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Key Features of Linear Functions
Domain & Range
Intercepts (x & y)
Increasing/Decreasing
Extrema (Minimum/Maximum)
Rate of Change Back
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Intervals
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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
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Identifying Key Features of a Linear Function
Intercepts:X-intercept: The place on the x-axis
where the graph crosses the axis.-Ordered pair: (x, 0)
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Identifying Key Features of a Linear Function
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)
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Identifying Key Features of a Linear Function
Intercepts:y-intercept: The place on the y-axis
where the graph crosses the axis-Ordered pair: (0, y)
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Identifying Key Features of a Linear Function
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)
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Identifying Key Features of a Linear Function
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)
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Identifying Key Features of a Linear Function
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)
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Identifying Key Features of a Linear Function
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
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Identifying Key Features of a Linear Function
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.
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Identifying Key Features of a Graph
The function is positive when x > ?
When x ≥ 4! Or [4, ∞)
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Identifying Key Features of a Graph
The function is negative when x < ?
When x < 4! Or (-∞, 4)
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Identifying Key Features of a Linear Function
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.
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Identifying Key Features of a Linear Function
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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
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Identifying Rate of Change
Identify two points on the line.(0, 2) and (5, 1)Use the formula:
51
0521
12
12
xxyym
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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
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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.
Identify the following:1. Type of function2. Domain and Range3. Y-intercept4. Intervals of Increasing
or Decreasing 5. Extrema6. Rate of Change
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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
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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.
Identify the following:1. Type of function2. Domain and Range3. Y-intercept4. Intervals of Increasing
or Decreasing 5. Extrema6. Rate of Change
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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.
Identify the following:1. Type of function2. Domain and Range3. Y-intercept4. Intervals of Increasing or
Decreasing 5. Extrema6. Rate of Change
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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.
Identify the following:1. Type of function2. Domain and Range3. Y-intercept4. Intervals of Increasing or
Decreasing 5. Extrema6. Rate of Change
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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.