Download Over Lesson 1–7

Over Lesson 1–7
Is the relation a function?
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B. B
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Over Lesson 1–7
A. Is
A the relation a function?
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Over Lesson 1–7
Is the relation {(7, 0), (0, 7), (–7, 0), (0, –7)}
a function?
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B. B
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Over Lesson 1–7
Is the relation y = 6 a function?
A. A
B. 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.
• 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.
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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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.
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. 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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Hypothesis: We are bowling.
Conclusion: It is Friday.
If we are bowling, it is Friday.
Hypothesis: It is Thursday.
Conclusion: We go bowling.
If it is Thursday, we go bowling.
Hypothesis: It is Friday.
Conclusion: We go bowling.
If it is Friday, then we go bowling.
Hypothesis: It is Friday.
Conclusion: We go bowling.
If it is not Thursday, we go bowling.
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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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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
Conclusion: x < 3
If 3x > 9, then x < 3.
D. Hypothesis: 11 + 5x < 21
Conclusion: x < 6
If 11 + 5x < 21, x < 6.
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
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.
Counterexamples
B. Find a counterexample for the conditional
statement below.
If Chloe is riding the Ferris wheel, then she is at the
State Fair.