over lesson 1–7 a.a b.b 5-minute check 1 is the relation a function?
TRANSCRIPT
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Over Lesson 1–7
A. A
B. B
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Is the relation a function?
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Over Lesson 1–7
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B. B
Is the relation a function?
A B
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x y
16 –8
12 –6
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–4 2
–10 5
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Over Lesson 1–7
A. A
B. B
Is the relation {(7, 0), (0, 7), (–7, 0), (0, –7)} a function?
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Over Lesson 1–7
A. A
B. B
Is the relation y = 6 a function?
A B
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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.
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• conditional statement
• if-then statements
• Hypothesis
• Conclusion
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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.
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Identify Hypothesis and Conclusion
B. Identify the hypothesis and conclusion of the statement.
If 7y + 5 = 26, then y = 3.
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A. Identify the hypothesis and conclusion of the statement. If it is above 75°, then you can go swimming.
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B. Identify the hypothesis and conclusion of the statement. If 2x + 3 = 5, then x = 1.
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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.
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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.
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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.
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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.
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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.
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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
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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.
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Counterexamples
B. Find a counterexample for the conditional statement below.
If Chloe is riding the Ferris wheel, then she is at theState Fair.