Download B. - V-SVHS

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
Is the relation a function?
A. yes
A. A
B. B
A
0%
0%
B
B. no
Over Lesson 1–7
A. Is
A the relation a function?
B. B x
y
16
–8
12
–6
0
0
–4
2
–10
5
A. yes
0%
B
B. no
A
0%
Over Lesson 1–7
Is the relation {(7, 0), (0, 7), (–7, 0), (0, –7)}
a function?
A. yes
A. A
B. B
A
0%
0%
B
B. no
Over Lesson 1–7
Is the relation y = 6 a function?
A. yes
B. no
A. A
B. B
0%
B
A
0%
Over Lesson 1–7
If f(x) = 3x + 7, find f(10).
A. 20
B. 23
A
B
C
0%
D
D
0%
B
0%
A
D. 37
C
C. 32
A.
B.
C.
0%
D.
Over Lesson 1–7
If g(x) = –2x – 2, find g(–2x).
C.
g(–2x) = 4x2
D.
g(–2x) = 4x2 – 2
0%
0%
A.
B.
C.
0%
D.
A
B
C
0%
D
D
g(–2x) = 4x2 + 4
C
B.
B
g(–2x) = 4x – 2
A
A.
Over Lesson 1–7
What
is the range shown in this function table?
A
B
C
D
x
4x + 5
y
–2
4(–2) + 5
–3
0
4(0) + 5
5
1
4(1) + 5
9
A. {–3, 5, 9}
B. {–8, 0, 4}
C. {3, 5, 6}
0%
D
0%
C
D. {–2, 0, 1}
0%
B
0%
A
A.
B.
C.
D.
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.
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.
Answer: Hypothesis: It is raining.
Conclusion: 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.
Answer: Hypothesis: 7y + 5 = 26
Conclusion: y = 3
A. Identify the hypothesis and conclusion of
the statement.
If it is above 75°, then you can go swimming.
C. Hypothesis: it is above 75°
Conclusion: you can go swimming
0%
B
0%
A
D. Hypothesis: it is 65°
Conclusion: you cannot go
swimming
A.
B.
C.
D.
A
B
C
D
D
B. Hypothesis: it is above 80°
Conclusion: you can go swimming
C
A. Hypothesis: you can go swimming
Conclusion: it is above 75°
0%
0%
B. Identify the hypothesis and conclusion of
the statement.
If 2x + 3 = 5, then x = 1.
C. Hypothesis: x + 3 = 4
Conclusion: x = 1
0%
B
0%
A
D. Hypothesis: 2x + 3 = 5
Conclusion: x = 1
A.
B.
C.
D.
A
B
C
D
D
B. Hypothesis: 2x + 6 = 12
Conclusion: x = 3
C
A. Hypothesis: x = 1
Conclusion: 2x + 3 = 5
0%
0%
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 = 43
Conclusion: a = 7
If 8 + 5a = 43, then a = 7.
A. Identify the hypothesis and conclusion of the
statement. Then write the statement in if-then form.
We go bowling on Fridays.
0%
0%
A
B
C
0%
D
D
D.
A.
B.
C.
0%
D.
C
C.
B
B.
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.
A
A.
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.
A
B
C
0%
D
D
A.
B.
C.
0%
D.
C
0%
B
0%
A
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
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.
C. The number is divisible by 3.
0%
B
0%
A
D. no valid conclusion
A
B
C
0%
D
D
B. The number is divisible by 10.
A.
B.
C.
0%
D.
C
A. The number is divisible by 2.
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.
C. The number is divisible by 2.
0%
B
0%
A
D. no valid conclusion
A
B
C
0%
D
D
B. The number is divisible by 10.
A.
B.
C.
0%
D.
C
A. The number is divisible by 9.
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.
Answer: x = 1, y = 2
Counterexamples
B. Find a counterexample for the conditional
statement below.
If Chloe is riding the Ferris wheel, then she is at the
State Fair.
Answer: Chloe could be riding a Ferris wheel at an
amusement park.
Which numbers are counterexamples for the
statement below?
If x ≤ 1, then x ● y ≤ 1.
A.
0%
B
D.
A
0%
A
B
C
0%
D
D
C.
C
B.
A.
B.
C.
0%
D.