1. Unit 3 Day 10 – Transformations of Logarithmic Functions

2. Warm Up 3
Describe the transformation!

3. Definitions
Domain
The x values!
Range
The y values!

4. is a line that a graph approaches, but does not intersect
Asymptote:
is a line that a graph approaches, but does not intersect

5. Asymptotes
Exponential functions will always have a horizontal asymptote (y = #) Logarithmic functions will always have a vertical asymptote (x = #)

6. X – intercept Y – intercept Where you cross the x – axis!
Where you cross the y – axis!

7. Exponential Function Logarithmic Function
A model to model exponential growth or decay
In the form
Logarithmic Function
The inverse of an exponential Function
In the form :

8. Look at # 1 and # 2

9. Transformations of Logarithmic Functions
Parent Function
y = logbx
Shift up
y = logbx + k
Shift down
y = logbx - k
Shift left
y = logb(x + h)
Shift right
y = logb(x - h)
Combination Shift
y = logb(x ± h) ± k
Reflect over the x-axis
y = -logbx
Stretch vertically
y = a logbx
Stretch horizontally
y = logbax

10. y = log (x + 2) y = log (x) – 3 y = 5 log x y = log (3x) y = -log x
Translations of logarithmic functions are very similar to those for other functions. Describe each translation for parent function y = log x.
y = log (x + 2)
y = log (x) – 3
y = 5 log x
y = log (3x)
y = -log x
y = log (x – 4) + 5
Left 2
Down 3
Vertical stretch by 5
Horizontal stretch by 3
Reflect over x-axis
Right 4, up 5

11. Description of transformations:
Graph the following function on the graph at right. Describe each transformation, give the domain and range, and identify any asymptotes.
y = -2log10(x + 2) – 4
Domain:
Range:
Asymptote:
Description of transformations:

12. Guided Practice

13. Homework
Independent Practice with Logarithmic Functions