Five-Minute Check (over Lesson 1–7)

Then/Now

New Vocabulary

Example 1:Identify Hypothesis and Conclusion

Example 2:Write a Conditional in If-Then Form

Example 3:Deductive Reasoning

Example 4:Counterexamples

Over Lesson 1–7

A. A

B. B

A. yes

B. no

A B

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Is the relation a function?

Over Lesson 1–7

A. A

B. B

A. yes

B. no

Is the relation a function?

A B

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x y

16 –8

12 –6

0 0

–4 2

–10 5

Over Lesson 1–7

A. A

B. B

A. yes

B. no

Is the relation {(7, 0), (0, 7), (–7, 0), (0, –7)} a function?

A B

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Over Lesson 1–7

A. A

B. B

A. yes

B. no

Is the relation y = 6 a function?

A B

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Over Lesson 1–7

A. A

B. B

C. C

D. D A B C D

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A. 20

B. 23

C. 32

D. 37

If f(x) = 3x + 7, find f(10).

Over Lesson 1–7

A. A

B. B

C. C

D. D A B C D

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A. g(–2x) = 4x – 2

B. g(–2x) = 4x2 + 4

C. g(–2x) = 4x2

D. g(–2x) = 4x2 – 2

If g(x) = –2x – 2, find g(–2x).

Over Lesson 1–7

A. A

B. B

C. C

D. D

A B C D

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A. {–3, 5, 9}

B. {–8, 0, 4}

C. {3, 5, 6}

D. {–2, 0, 1}

What is the range shown in this function table?

x 4x + 5 y

–2 4(–2) + 5 –3

0 4(0) + 5 5

1 4(1) + 5 9

You applied the properties of real numbers. (Lesson 1–3)

• Identify the hypothesis and conclusion in a conditional statement.

• Use a counterexample to show that an assertion is false.

• conditional statement

• if-then statements

• hypothesis

• conclusion

• deductive reasoning

• counterexample

Identify Hypothesis and Conclusion

A. Identify the hypothesis and conclusion of the statement.

SPORTS If it is raining, then Jon and Urzig will not play softball.

Answer: Hypothesis: It is raining.Conclusion: Jon and Urzig will not play softball.

Recall that the hypothesis is the part of the conditional following the word if and the conclusion is the part of the conditional following the word then.

Identify Hypothesis and Conclusion

B. Identify the hypothesis and conclusion of the statement.

If 7y + 5 = 26, then y = 3.

Answer: Hypothesis: 7y + 5 = 26 Conclusion: y = 3

A. A

B. B

C. C

D. D A B C D

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A. Hypothesis: you can go swimming Conclusion: it is above 75°

B. Hypothesis: it is above 80° Conclusion: you can go swimming

C. Hypothesis: it is above 75° Conclusion: you can go swimming

D. Hypothesis: it is 65° Conclusion: you cannot go swimming

A. Identify the hypothesis and conclusion of the statement. If it is above 75°, then you can go swimming.

A. A

B. B

C. C

D. D A B C D

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A. Hypothesis: x = 1 Conclusion: 2x + 3 = 5

B. Hypothesis: 2x + 6 = 12

Conclusion: x = 3

C. Hypothesis: x + 3 = 4 Conclusion: x = 1

D. Hypothesis: 2x + 3 = 5 Conclusion: x = 1

B. Identify the hypothesis and conclusion of the statement. If 2x + 3 = 5, then x = 1.

Write a Conditional in If-Then Form

A. Identify the hypothesis and conclusion of the statement. Then write the statement in if-then form.

I eat light meals.

Answer: Hypothesis: I eat a meal.Conclusion: It is light.If I eat a meal, then it is light.

Write a Conditional in If-Then Form

B. Identify the hypothesis and conclusion of the statement. Then write the statement in if-then form.

For the equation 8 + 5a = 43, a = 7.

Answer: Hypothesis: 8 + 5a = 43Conclusion: a = 7If 8 + 5a = 43, then a = 7.

A. A

B. B

C. C

D. D A B C D

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A. Hypothesis: We are bowling.Conclusion: It is Friday.If we are bowling, it is Friday.

B. Hypothesis: It is Thursday.Conclusion: We go bowling.If it is Thursday, we go bowling.

C. Hypothesis: It is Friday.Conclusion: We go bowling.If it is Friday, then we go bowling.

D. Hypothesis: It is Friday.Conclusion: We go bowling.If it is not Thursday, we go bowling.

A. Identify the hypothesis and conclusion of the statement. Then write the statement in if-then form.We go bowling on Fridays.

A. A

B. B

C. C

D. D A B C D

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A. Hypothesis: x < 2Conclusion: 11 + 5x < 21If x < 2, 11 + 5x < 21.

B. Hypothesis: 11 + 5x < 21 Conclusion: x < 2. If 11 + 5x < 21, then x < 2.

C. Hypothesis: 3x < 9Conclusion: x < 3If 3x > 9, then x < 3.

D. Hypothesis: 11 + 5x < 21 Conclusion: x < 6If 11 + 5x < 21, x < 6.

B. Identify the hypothesis and conclusion of the statement. Then write the statement in if-then form.For the inequality 11 + 5x < 21, x < 2.

Deductive Reasoning

A. Determine a valid conclusion that follows from the statement, “If one number is odd and another number is even, then their sum is odd” for the given conditions. If a valid conclusion does not follow, write no valid conclusion and explain why.

The two numbers are 5 and 12.

5 is odd and 12 is even, so the hypothesis is true.

Answer: Conclusion: The sum of 5 and 12 is odd.

Deductive Reasoning

B. Determine a valid conclusion that follows from the statement, “If one number is odd and another number is even, then their sum is odd” for the given conditions. If a valid conclusion does not follow, write no valid conclusion and explain why.

The two numbers are 8 and 26.

Both numbers are even, so the hypothesis is false.

Answer: no valid conclusion

A. A

B. B

C. C

D. D A B C D

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A. The number is divisible by 2.

B. The number is divisible by 10.

C. The number is divisible by 3.

D. no valid conclusion

A. Determine a valid conclusion that follows from the statement “If the last digit in a number is 0, then the number is divisible by 10” for the given conditions. If a valid conclusion does not follow, write no valid conclusion.

The number is 16,580.

A. A

B. B

C. C

D. D A B C D

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A. The number is divisible by 9.

B. The number is divisible by 10.

C. The number is divisible by 2.

D. no valid conclusion

B. Determine a valid conclusion that follows from the statement “If the last digit in a number is 0, then the number is divisible by 10” for the given conditions. If a valid conclusion does not follow, write no valid conclusion.

The number is 4,005.

Counterexamples

A. Find a counterexample for the conditional statement below.

x + y > xy, then x > y.

Answer: x = 1, y = 2

One counterexample is when x = 1 and y = 2. The hypothesis is true, 1 + 2 > 1 ● 2. However, the conclusion 1 > 2 is false.

Counterexamples

B. Find a counterexample for the conditional statement below.

If Chloe is riding the Ferris wheel, then she is at theState Fair.

Answer: Chloe could be riding a Ferris wheel at an amusement park.

A. A

B. B

C. C

D. D A B C D

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Which numbers are counterexamples for the statement below?If x ≤ 1, then x ● y ≤ 1.

A.

B.

C.

D.