Five-Minute Check (over Lesson 2–5)

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

A. A

B. B

C. C

D. D A B C D

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Which scatter plot represents the data shown in the table?

A. B.

C. D.

Over Lesson 2–5

A. A

B. B

C. C

D. D A B C D

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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

A. A

B. B

C. C

D. D A B C D

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A. $62

B. $72

C. $82

D. $92

Use your prediction equation to predict the missing value.

Over Lesson 2–5

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

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.

You modeled data using lines of regression. (Lesson 2–5)

• 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 Graph the linear function f(x) = x –1 for x ≤ 3. Since 3 satisfies this inequality, begin with a closed circle at (3, 2).

Piecewise-Defined Function

Step 2 Graph the constantfunction f(x) = –1 forx > 3. Since x doesnot satisfy thisinequality, begin withan open circle at(3, –1) and draw ahorizontal ray to theright.

Piecewise-Defined Function

Answer: The function is defined for all values of x, so the domain is all realnumbers. The values that arey-coordinates of points on thegraph are all real numbersless than or equal to 2, so therange is {y | y ≤ 2}.

A. A

B. B

C. C

D. D A B C D

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A. domain: all real numbersrange: all real numbers

B. domain: all real numbersrange: {y|y > –1}

C. domain: all real numbersrange: {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.

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}.

Write a Piecewise-Defined Function

Write the piecewise-defined function.

Answer:

A. A

B. B

C. C

D. D A B C D

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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 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.

Use a Step Function

Solve 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

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.

A. A

B. B

C. C

D. D A B C D

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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.

x |x| + 1

–3 4

–2 3

–1 2

0 1

1 2

2 3

3 4

Absolute Value Functions

Graph the points and connect them.

Answer:The domain is all realnumbers. The range is {y | y ≥ 1}.

A. A

B. B

C. C

D. D A B C D

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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.