Over Lesson 1–7 A.A B.B 5-Minute Check 1 Is the relation a function?

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Over Lesson 1–7 A.A B.B 5-Minute Check 1 Is the relation a function?

Over Lesson 1–7 5-Minute Check 2 A.A B.B Is the relation a function? xy 16–8 12–6 00 –42 –105

Over Lesson 1–7 A.A B.B 5-Minute Check 3 Is the relation {(7, 0), (0, 7), (–7, 0), (0, –7)} a function?

Over Lesson 1–7 A.A B.B 5-Minute Check 4 Is the relation y = 6 a function?

Then/Now 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.

Vocabulary conditional statement if-then statements Hypothesis Conclusion

deductive reasoning counterexample

Example 1 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.

Example 1 Identify Hypothesis and Conclusion B. Identify the hypothesis and conclusion of the statement. If 7y + 5 = 26, then y = 3.

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

Example 2 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.

Example 2 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.

A.A B.B C.C D.D Example 2 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 Example 2 A.Hypothesis: x < 2 Conclusion: x < 21 If x < 2, x < 21. B.Hypothesis: x < 21 Conclusion: x < 2. If x < 21, then x < 2. C.Hypothesis: 3x 9, then x < 3. D.Hypothesis: x < 21 Conclusion: x < 6 If x < 21, x < 6. B. Identify the hypothesis and conclusion of the statement. Then write the statement in if-then form. For the inequality x < 21, x < 2.

Example 3 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 is odd and 12 is even, so the hypothesis is true. Answer: Conclusion: The sum of 5 and 12 is odd.

Example 3 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

Example 4 Counterexamples A. Find a counterexample for the conditional statement below. x + y > xy, then x > y. One counterexample is when x = 1 and y = 2. The hypothesis is true, > 1 ● 2. However, the conclusion 1 > 2 is false.

Example 4 Counterexamples B. Find a counterexample for the conditional statement below. If Chloe is riding the Ferris wheel, then she is at the State Fair.