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Lesson Menu 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 5-Minute Check 1 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 5-Minute Check 1 Which scatter plot represents the data shown in the table? A.B. C.D.

Over Lesson 2–5 5-Minute Check 2 A.y = 2x + 94 B.y = 2x + 64 C.y = –2x + 94 D.y = –2x + 64 Which prediction equation represents the data shown in the table?

Over Lesson 2–5 5-Minute Check 3 A.$62 B.$72 C.$82 D.$92 Use your prediction equation to predict the missing value.

Over Lesson 2–5 5-Minute Check 4 A.6 B.12 C.24 D.48 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.

CCSS 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.

Then/Now You modeled data using lines of regression. Write and graph piecewise-defined functions. Write and graph step and absolute value functions.

Vocabulary piecewise-defined function piecewise-linear function step function greatest integer function absolute value function

Example 1 Piecewise-Defined Function Step 1Graph the linear function f(x) = x – 1 for x ≤ 3. Since 3 satisfies this inequality, begin with a closed circle at (3, 2).

Example 1 Piecewise-Defined Function Step 2Graph the constant function f(x) = –1 for x > 3. Since x does not satisfy this inequality, begin with an open circle at (3, –1) and draw a horizontal ray to the right.

Example 1 Piecewise-Defined Function Answer: The function is defined for all values of x, so the domain is all real numbers. The values that are y-coordinates of points on the graph are all real numbers less than or equal to 2, so the range is {f(x) | f(x) ≤ 2}.

Example 1 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

Example 2 Write a Piecewise-Defined Function Write the piecewise-defined function shown in the graph. Examine and write a function for each portion of the graph. The left portion of the graph is a graph of f(x) = x – 4. There is a circle at (2, –2), so the linear function is defined for {x | x < 2}. The right portion of the graph is the constant function f(x) = 1. There is a dot at (2, 1), so the constant function is defined for {x | x ≥ 2}.

Example 2 Write a Piecewise-Defined Function Write the piecewise-defined function. Answer:

Example 2 Identify the piecewise-defined function shown in the graph. A. B. C. D.

Example 3 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 The total charge must be a multiple of $85, so the graph will be the graph of a step function. Plan 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.

Example 3 Use a Step Function SolveUse 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.

Example 3 Use a Step Function Answer: Check Since the psychologist rounds any fraction of an hour up to the next whole number, each segment on the graph has a circle at the left endpoint and a dot at the right endpoint.

Example 3 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.

Concept

Example 4 Absolute Value Functions Graph y = |x| + 1. Identify the domain and range. Create a table of values. x|x| + 1 –34 –23 –

Example 4 Absolute Value Functions Graph the points and connect them. Answer: The domain is all real numbers. The range is {y | y ≥ 1}.

Example 4 A.y = |x| – 1 B.y = |x – 1| – 1 C.y = |x – 1| D.y = |x + 1| – 1 Identify the function shown by the graph.

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