& Notes: Change of Base DAY # 12 5.2.4 # 85 87 Math 3€¦ · 5.2.4 # 85 → 87 & Notes: Change of...
Transcript of & Notes: Change of Base DAY # 12 5.2.4 # 85 87 Math 3€¦ · 5.2.4 # 85 → 87 & Notes: Change of...
5.2.4 # 85 → 87 & Notes: Change of BaseTuesday, February 4, 2020 &Wednesday, February 5, 2020
Math 3DAY # 12
5
112/3
Inverses Exam ● Exam None
Investigating the family of log functions
● Practice● 5.2.3
Work on inverses practice
101/301/31
Investigating Logarithmic Functions
● Notes● 5.2.2 #63→65
91/281/29
Quiz Corrections
2
122/42/5
How can I transform a logarithmic function?
● 5.2.4 ● Notes Checkpoint #7
Choose 5
132/62/7
Properties of Logarithms
● Logs Prac. #1● 7.1.1 #1→5
Logs Practice
Prerequisites LEARNING PLAN #1 (Ch.1)Prerequisites TOOLKIT #1 (ch.1)
1-Variable Data TOOLKIT #2 (Ch.1)
1-Variable Data LEARNING PLAN #2 (Ch.1)
Calculator Instructions for Statistics
Transforming Parabolas (Ch.2)Averaging the x-intercepts (Ch.2)
Transformations TOOLKIT #3 (Ch.2)
Families of Functions Graphic Organizer (Ch.2)Ch. 2 Practice Quiz
Transformations LEARNING PLAN #3 (Ch.2)Solving Equations LEARNING PLAN #4 (Ch.3)Equations & Inequalities TOOLKIT #4/5 (Ch.3)Inequalities LEARNING PLAN #5 (Ch.3)
FINAL EXAM Study GuideInverses LEARNING PLAN #6 (Ch.5)Inverses TOOLKIT #6 (Ch.5)Exponentials TOOLKIT #7
Nothing new!
Logarithms LEARNING PLAN #8 (Ch.5 & 7)Logarithms TOOLKIT #8
6
Unit 6: Inverses, Unit 7: Exponentials & Unit 8: Logarithms
1 5.1.1 # 1→ 5 1/7 or 1/8
2 5.1.2 # 15→ 23 1/9 or 1/10
Nothing New!
3 Inverses Practice Packet 1/13
5.1.3 #40 → 434 1/14 or 1/15
Exponentials Practice Packet5 1/23 or 1/24
5.2.1 # 53 → 556 1/23 or 1/24
5.2.2 # 63 → 657 1/28 or 1/29
5.2.3 function investigation8 1/30 or 1/31
5.2.4 #85 → 879 2/4 or 2/5
7.1.1 #1 → 5
10
2/6 or 2/7
Logarithms Practice #1
11
2/6 or 2/7
5 Thursday/Friday 2/6 or 2/7
Logarithm Form: y = log3(x)
Exponential Form:
Make a table and a complete graph the function.
x
y
BONUS: graph y = log3(x + 4) without making a table.
⅓ -1
10
31
92
x = 3y
Announcements:● If you missed the Inverses Exam on Monday,
talk with Ms. Ramer ASAP to arrange for a make-up.
● Monday is a B-Day! No school next Friday.● Next Quiz is Weds/Thurs, February 12th/13th
Stamps! B-Page: 5/6C-Page: C2CW#9: 5.2.4 #85→87
Late work?● C-Page #1 or #2???
● C-Page #3???
Let’s look at what we did last class...
Turn to the bottom of the 2nd page.
CW#9
Think about the other functions we’ve learned about.... Parabolas: y = x2 → y = a(x - h)2 + k
Cubics: y = x3 → y = a(x - h)3 + k
Absolute Value: y = |x| → y = a|x - h| + k
Parabolas: y = x2 → y = a(x - h)2 + k
Cubics: y = x3 → y = a(x - h)3 + k
Absolute Value: y = |x| → y = a|x - h| + k
y = a · logb(x - h) + k
Vertical Stretch/Compression & Orientation
Horizontal Translation
Vertical Translation“Base” also affects Stretch /Compression & Orientation, but in a different way.
Desmos Tool:
Let’s try 87 b together:
h = 2Translated 2 units horizontally
It’s like shifting the axes over 2 units to the right. Graph the
parent function on “new” x-y axes
Parent is y = log (x) same as 10y = x
Asymptote x = 2
You need:● Pencil● Logarithms
Toolkit (G20)
19Bottom of 1st page.
10
log10(4)
102
log10100 = 2
(23)x = (25)(x-6) 23x = 2(5x - 30) → 3x = 5x - 30
Is equivalent to 2y = x
Top of 2nd page.
Take a few minutes to fill out the table and description with your team.
Is equivalent to 2y = x
-2 -1 0 1 2 4
logarithmicVertical @ x = 0
No symmetryx-int @ (1,0), no y-int
x > 0-∞ < y < ∞
You need:● Pencil● Calculator ● Toolkit● Logarithms
Practice #1
You need:● Pencil● Graphing
Calculator● 7.1.1 worksheet
11
Facilitators: Read aloud to get your team started. Discuss ideas before writing.
Logs are related to exponents.
For logb(a) = c:
b is the base, c is the exponent and a is what it’s all equal to.
The base is 10!→ when you use [log] button on calculator&→ when the base isn’t written
It’s the inverse of an exponential. (w/ a vertical asymptote)
y = a·log(x - h) + k
Move on to #2!
Recorder/Reporters: Check your team’s graphs.
Facilitators: Read aloud! Share ideas.
Task Manager: Keep an eye on the time.
Resource Manager: Everyone uses calculators.
Graphing form of a logarithm is similar to graphing for for the other families of functions because...
I can graph a log function more easily by…
The property of logs we learned about today was...
Choose one or two.
Clean up!!● Put classwork in binder● Pack up your stuff● Put away supplies & clean your area● Straighten desks
● Stay seated w/ backpack off until you’re dismissed