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Five-Minute Check (over Lesson 2–5) CCSS Then/Now New Vocabulary Example 1: Piecewise-Defined Function Example 2: Write a Piecewise-Defined Function Example 3: Real-World Example: Use a Step Function Key Concept: Parent Functions of Absolute Value Functions Example 4: Absolute Value Functions Over Lesson 2–5 Sketch a scatter plot to represent the data shown in the table. Develop a prediction equation for the data shown in the table. Use your prediction equation to predict the missing value. The scatter plot shows the number of summer workouts the players on a basketball team attended and the number of wins during the following season. Predict the number of wins the team would have if they attended 24 summer workouts. Over Lesson 2–5 Which scatter plot represents the data shown in the table? A. B. C. D. Over Lesson 2–5 Which prediction equation represents the data shown in the table? A. y = 2x + 94 B. y = 2x + 64 C. y = –2x + 94 D. y = –2x + 64 Over Lesson 2–5 Use your prediction equation to predict the missing value. A. $62 B. $72 C. $82 D. $92 Over Lesson 2–5 The scatter plot shows the number of summer workouts the players on a basketball team attended and the number of wins during the following season. Predict the number of wins the team would have if they attended 24 summer workouts. A. 6 B. 12 C. 24 D. 48 Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. F.IF.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Mathematical Practices 1 Make sense of problems and persevere in solving them. You modeled data using lines of regression. • Write and graph piecewise-defined functions. • Write and graph step and absolute value functions. • piecewise-defined function • piecewise-linear function • step function • greatest integer function • absolute value function Piecewise-Defined Function Step 1 Step 2 Graph the linear function f(x) = x – 1 for x ≤ 3. Graph the constant function f(x) = –1 for x > 3. Answer: The domain is all real numbers. The range is {f(x) | f(x) ≤ 2}. A. domain: all real numbers range: all real numbers B. domain: all real numbers range: {y|y > –1} C. domain: all real numbers range: {y|y > –1 or y = –3} D. domain: {x|x > –1 or x = –3} range: all real numbers Write a Piecewise-Defined Function Write the piecewise-defined function shown in the graph. The left portion of the graph is a graph of f(x) = x – 4. The linear function is defined for {x | x < 2}. The right portion of the graph is the constant function f(x) = 1. The constant function is defined for {x | x ≥ 2}. Answer: Identify the piecewise-defined function shown in the graph. A. B. C. D. Use a Step Function PSYCHOLOGY One psychologist charges for counseling sessions at the rate of $85 per hour or any fraction thereof. Draw a graph that represents this situation. Understand If the session is greater than 0 hours, but less than or equal to 1 hour, the cost is $85. If the time is greater than 1 hour, but less than or equal to 2 hours, then the cost is $170, and so on. The total charge must be a multiple of $85, so the graph will be the graph of a step function. Use a Step Function PSYCHOLOGY One psychologist charges for counseling sessions at the rate of $85 per hour or any fraction thereof. Draw a graph that represents this situation. Plan Use the pattern of times and costs to make a table, where x is the number of hours of the session and C(x) is the total cost. Then draw the graph. Use a Step Function PSYCHOLOGY One psychologist charges for counseling sessions at the rate of $85 per hour or any fraction thereof. Draw a graph that represents this situation. Solve Graph SALES The Daily Grind charges $1.25 per pound of meat or any fraction thereof. Draw a graph that represents this situation. A. B. C. D. Absolute Value Functions Graph y = |x| + 1. Identify the domain and range. Create a table of values. Graph the points and connect them. x |x| + 1 –3 4 –2 3 –1 2 0 1 1 2 2 3 3 4 The domain is all real Answer: numbers. The range is {y | y ≥ 1}. Identify the function shown by the graph. A. y = |x| – 1 B. y = |x – 1| – 1 C. y = |x – 1| D. y = |x + 1| – 1