Uploaded on

 

  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
    Be the first to like this
No Downloads

Views

Total Views
202
On Slideshare
0
From Embeds
0
Number of Embeds
0

Actions

Shares
Downloads
4
Comments
0
Likes
0

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 1. 1  An example of an exponential function is:____________________________  What would the inverse of that function look like?  Now we need to solve for y. In order to change x b y to proper form, new terminology had to be created by mathematicians. Therefore the word ________________________ is used in place of exponent. Exponential Form Logarithmic Form  Graphing Sketch y 2x Sketch the inverse of y 2x y y x x
  • 2. 2  y 2 x and ___________________ are inverses.  x 2 y is equal to __________________, therefore, this is the graph of a logarithmic function. Graph (hint: convert to exponential form first) f ( x) log3 x f ( x) log 1 x 2 y y x x Characteristics:  Domain:__________________________  Range:____________________________  ________________________ function  Common point: _____________ therefore, the x intercept would be __________.  There is not a ____________. Therefore there is a vertical asymptote at ________  If b > 1, the function is ___________________  If 0 < b < 1, the function is ________________
  • 3. 3 Sketch: f ( x) log 4 (3 x) Hint: if you are using a table of values convert to exponential form first (switch and factor). x f(x) y x Interchanging Log and Exponential Forms Log Form Exponential Form log5 25 2  Remember that y log a x Evaluate: 1. y log9 27 hint: convert to exponential form and solve
  • 4. 4 3 2. log b 4 3. log 2 (log3 9) x FYI: Logs which are to the base of 10 are called __________________________ Calculators are set up to deal with base 10 logs. It is often written without the “10” (x = log y) Evaluate: log10 100 Without Calculator With Calculator
  • 5. 5 Transformations: State how each of the equations below transforms the graph of f ( x) loga x 1) f ( x) log2 ( x 1) 2) f ( x) log3 ( x 5) 3) f ( x) log 4 ( x) 3 4) f ( x) log5 ( x) 2 5) f ( x) log3 (1 x) 6) f ( x) log 2 (4 x) 1 7) f ( x) log 4 (3 x) On Your Own Sketch f ( x) log 4 (3 x) **Remember to change it to exponential form first! 4y x 4y x 3 y x y x y x
  • 6. 6 On Your Own Sketch f ( x) log 2 ( x 1) 3 **Remember to change it to exponential form first! y x