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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. Common Core Georgia Performance Standard: MCC9–12.F.IF.4; MCC9–12.F.IF.5 3.3.1: Identifying Key Features of Linear and Exponential Graphs

Use the graph to describe Kim’s journey. What do the horizontal lines on the graph represent? 3.3.1: Identifying Key Features of Linear and Exponential Graphs

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. 3.3.1: Identifying Key Features of Linear and Exponential Graphs

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. Connection to the Lesson Students will extend their understanding of graphs and begin to more formally describe various features. Students will be asked to interpret key features from graphs and tables as well as sketch graphs given a verbal description. 3.3.1: Identifying Key Features of Linear and Exponential Graphs

Lesson 3.4 – Characteristics of Linear Functions Concepts: Characteristics of Linear Functions EQ: What are the key features of a linear function? (Standard F.IF.7) Vocabulary: Rate of change Domain/Range x and y intercepts Intervals of Increasing/Decreasing Extrema (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 values Range: all possible output values Example: 𝟏,𝟒 , 𝟐, 𝟓 , (𝟑, 𝟔) Domain: 1, 2, 3 Range: 4, 5, 6

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)

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 + 2 0 = x +2 -2 = x x-intercept: (-2, 0)

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)

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 + 2 y = 0 +2 y = 2 y-intercept: (0, 2)

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)

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)

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

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.

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)

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.

Identifying Key Features of a Linear Function

Identifying 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.

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

Example 1: Guided Practice Example 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: Type of function Domain and Range Y-intercept Intervals of Increasing or Decreasing Extrema Rate of Change

Example 2: Identify the following: Type of function Domain and Range Y-intercept Intervals of Increasing or Decreasing Extrema Rate of Change 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: Identify the following: Type of function Domain and Range Y-intercept Intervals of Increasing or Decreasing Extrema Rate of Change An online company charges $5.00 a month plus $2.00 for each movie you decide to download.

Example 4: Identify the following: Type of function Domain and Range Y-intercept Intervals of Increasing or Decreasing Extrema Rate of Change 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 1 The 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: Type of function Domain and Range Y-intercept Intervals of Increasing or Decreasing Extrema Rate of Change

You Try 2 Identify the following: Type of function Domain and Range Y-intercept Intervals of Increasing or Decreasing Extrema Rate of Change The 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.