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

2. 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

3. 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?

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

5. 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.

6. Vocabulary conditional statement if-then statements Hypothesis Conclusion

7. deductive reasoning counterexample

8. 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.

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

10. 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.

11. 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.

12. 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.

13. 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.

14. 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.

15. A.A B.B C.C D.D Example 2 A.Hypothesis: x < 2 Conclusion: 11 + 5x < 21 If x < 2, 11 + 5x < 21. B.Hypothesis: 11 + 5x < 21 Conclusion: x < 2. If 11 + 5x < 21, then x < 2. C.Hypothesis: 3x 9, then x < 3. D.Hypothesis: 11 + 5x < 21 Conclusion: x < 6 If 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.

16. 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 12. 5 is odd and 12 is even, so the hypothesis is true. Answer: Conclusion: The sum of 5 and 12 is odd.

17. 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

18. 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 > 1 ● 2. However, the conclusion 1 > 2 is false.

19. 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.