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Warm-Up: September 16, 2016 a) Complete the table: b) Is ݂ ݐlinear, quadratic, or exponential? c) Is ݃ ݐlinear, quadratic, or exponential? d) Write a recursive equation for ݂ ݐ. e) Write a recursive equation for ݃ ݐ.
࢚ ࢌ ࢚ = ࢚ ࢍ ࢚ = ࢚ 0 1 2 3 4 5 6
Module 1 Quiz and Test • Quiz is graded – check PowerSchool • If you did not take it, you should do so after school today or Monday. • Grades were bad. • If you do better on the test than the quiz, your quiz grade will be dropped. • Test postponed one week to Sep. 28.
Warm-Up: September 19, 2016 • Write both an explicit formula and a recursive formula for the data in the table to the right
ࢌ
0
3
1
1
2
−5
3
−15
4
−29
5
−47
6
−69
Section 1.6 Integrated Math 2
The Tortoise and the Hare A Solidify Understanding Task
The Tortoise and the Hare
• In the children’s story of the tortoise and the hare, the hare mocks the tortoise for being slow. The tortoise replies, “Slow and steady wins the race.” The hare says, “We’ll just see about that,” and challenges the tortoise to a race. Because the hare is so confident that he can beat the tortoise, he gives the tortoise a 1 meter head start.
• The hare’s distance from the starting line is given by ݀ = ݐଶ • The tortoise’s distance from the starting line is given by ݀௧ = 2௧ • For both formulas, ݀ is in meters and ݐis in seconds.
1
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The Tortoise and the Hare 1) At what time does the hare catch up to the tortoise? 2) If the race course is very long, who wins: the tortoise or the hare? Why? 3) At what time(s) are they tied? 4) If the race course were 15 meters long, who wins: the tortoise or the hare? Why?
y
19 18 17
7
y
16 15 14 13 12 11 10 9
6
5
4
3
2
1 x
8 7 6 5 4 3 2 1
−5
−4
−3
−2
−1
1
2
3
4
x
5
1
−1
The Tortoise and the Hare 5) Use the properties of ݀௧ = 2௧ and ݀ = ݐଶ to explain the speeds of the tortoise and the hare in the following time intervals: Interval Tortoise: ࢊ࢚ =
࢚
Hare: ࢊࢎ =
࢚
2
3
4
5
y 1000 900 800 700 600 500
0, 2
400 300
2, 4
200 100
4, ∞
x 1
2
3
4
5
6
7
8
9
2
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Assignment
Warm-Up: September 20, 2016 • Describe the domain (ݔ-values) and range (ݕ-values). y
• 1.6 Ready, Set, Go
y
5
a)
6
4 3 2 1 x 1
2
3
4
b) ࢞ 0 4 5
c) ࢟ 3 2 2
5 4 3 2 1 x
−2 −1 −1
1
2
3
4
5
6
−2
−1
−3
Interval Notation
Matching Activity
• Smallest number in interval, largest number in interval • Use [square brackets] to include the end value • Use (round brackets / parentheses) if end value should not be included • Always use ( ) with ±∞
• Work with your partner to match the domains and ranges with the graphs. • After you are finished, determine which are functions, and which are not functions. • Then, find the domain and range of the 9 graphs on the back.
3
