1. Inverses of Functions (logs and exponentials)
Unit 3 Day 12
Inverses of Functions (logs and exponentials)

2. Warm Up y = 1/15x + 1/15 y = 7/4x y = 3x - 21 y = 1/5x - 11/5
Extra one….I-123 is used in thyroid scans hours after the formation of a 45 mg sample, only 22.5 mg remain. How much of the I-123 will remain after 66 hours? Show your work algebraically.

3. 1. 3. 2. Homework Answers – Day 11 Comparison: Translated up 2
Comparison: reflected over the y-axis 2.
Comparison: Translated left 2 and down 3

4. HW continued…
4.) Shifted up 2 5.) reflected over the y-axis, shifted down 1 6.) vertical shrink by ¼ 7.) shifted left 2 and up 3 8.) reflected over the x-axis 9.) vertical stretch by 3, shifted down 4

5. HW continued…
1.) y = 3x – 3 3.) y = 1/2x – 5/2 5.) y = (x – 2)1/2 7.) y = x/3 – 1 9.) after about 16.9 years so = 2008

6. Homework: Day 12 Packet p. 17 and 18

7. The Richter Scale E∙308 308-6.8 301.3 = 59.23 E∙306.8 59.23
Work through this initial example with the class.
E∙308
301.3 = 59.23
E∙306.8
59.23

8. Logs

10. A little experiment… Partner 1 Partner 2
Graph y = 10x on one side of the graph paper.
(pick a good scale)
Use this table of points.
Help partner 1 with the first graph.
Make a new table by flipping the x’s and y’s from the y = 10x graph.
Graph on the other side of the graph paper. (pick a good scale) x y -2 -1 1 2

11. The log function is the inverse of the exponential function!
y = 10x and y = log10x

12. Hor. Asymptote
Vert. Asymptote

13. Translations of logs are just like other functions!!
Remember the two types of functions we have already translated:
y = 2(x - 2)2 + 3
y = 3x-2 + 3

14. Vertical Asymptote: x = 0
Domain: x > 0
Range: All real #s

15. Here’s a basic example…
*Not in Notes… do on graph paper
1.) log10(x+1)
x > -1
All real #s
x = -1
Left 1
Graph on calc
Look at the table for pts.
Plot

16. Another example… *Not in Notes… do on graph paper 2.) log10x + 1
All real #s
x = 0
Up 1

17. Harder example (in notes)…
All real #s
x = -2
Reflection over x axis, stretched
vertically by 2, left 2, down 4

18. Guided Practice with Logarithmic Functions
In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the amount of energy released by that earthquake to the amount of energy released by each earthquake below. 1) Magnitude 7.7 in San Francisco, California, in 1906.
2) Magnitude 3.2 in Charlottesville, Virginia, in 2001.
New Madrid was 1.97 times stronger.
New Madrid was times stronger.

19. Guided Practice with Logarithmic Functions
3) Magnitude 9.5 in Valdivia, Chile, in 1960.
4) How much stronger was the earthquake in Valdivia than the earthquake in San Francisco?
Valdivia was times stronger than New Madrid.
Valdivia was times stronger than San Francisco.

20. x > 0
All real #s
x = 0
Down 6

21. x > -2
All real #s
x = -2
Reflected over
x-axis and left 2

22. x > 0
All real #s
x = 0
2 times wider
(stretched horizontally)

23. Exit Ticket
Tell how the graphs on the board changed from the parent functions!!

24. Homework: Day 12 Packet p. 17 and 18