1. Vertical Line Test: Is the Graph a Function?

2. Horizontal Line Test: Is the Inverse of the Graph a Function?

3. Restricted Domain Inverse Function Inverse
Find the inverse function of f below:
Inverse Function
Inverse

4. Restricted Domain
Find the inverse function of f below:

5. Composition of Functions
Second g f
First
(inside parentheses always first) OR

6. Inverse and Compositions
In order for two functions to be inverses:
AND

7. Algebraically Finding an Inverse
Find the inverse functions of the following:

8. Day 42: November 5th
Objective: Apply strategies for finding inverses to parent graph equations. Begin to think of the inverse function for y=3x. THEN Define the term logarithm as the inverse exponential function or, when y=bx, “y is the exponent to use with base b to get x.”
Homework Check
6-54 to 6-58 (pgs )
Wells Time
6-67 to 6-71 (pgs )
Closure
Homework: 6-59 to 6-66 (pgs ) AND 6-72 to (pgs )
Project Due: Monday, November 8th 8

9. Silent Board Game

10. Silent Board Game

11. 6-71: Closure 2 4 7
1.2
w + 3

12. Logarithm's Undo Exponentials
Log’s give you exponents!
Inverses
Same as

13. Logarithm and Exponential Forms
y = log2(32)
2y = 32

14. Logarithms a > 0 b > 0
The logarithm base a of b is the exponent you put on a to get b.
i.e. Logs give you exponents!

15. Day 43: November 5th
Objective: Develop methods to graph logarithmic functions with different bases. Rewrite logarithmic equations as exponential equations and find inverses of logarithmic functions. THEN Look into the base of the log key on the calculator. Also extend our knowledge of general equations for parent functions to transform the graph of y=log(x).
Homework Check
6-81 and 6-83 (pgs )
Wells Time
6-93 and 6-95 (pgs )
Closure
Homework: 6-84 to 6-92 (pgs ) AND 6-96 to (pgs ) 15

16. 6-83: Learning Log What is the general shape of the graph?
Title: The Family of Logarithmic Functions
What is the general shape of the graph?
What happens to the value of y as x increases?
How is the graph related to the exponential graph?
What is the Domain? Range?
Why is the x-intercept always (1,0)?
Why is the line x=0 (y-axis) always an asymptote?
Why is there no horizontal asymptote?
How does the graph change if b changes?
What does the graph look like when 0<b<1?
What does the graph look like when b=1?
What does the graph look like when b>1? 16 16 16

17. Common Logarithm
Ten is the common base for logarithms, so log(x) is called a common logarithm and is shorthand for writing log10(x). You read this as “the logarithm base 10 of x.”
Our calculator has the button log . It doesn’t have the subscript 10 because it stands for the common logarithm:
log10100 = log100

18. Exponential Parent Equation: a General Equation: Domain: Range: y=k
x=h

19. Logarithms
Parent Equation:
General Equation:
y=k
Domain:
Range:
x=h

20. Day 44: November 9th Objective: Assess chapter 6 in a team setting.
Homework Check
Chapter 6 Team Test
Closure
Homework: to (pgs ) 20

21. Day 45: November 10th
Objective: Assess Chapters 1-5 in a individual setting.
Homework Check
Midterm Exam
Closure
Homework: 7-9 to 7-15 (pgs ) 21