1. Warm-up: Complete the absolute value column on your graphic organizer
𝒇 𝒙 = 𝒙
Domain
Range
End Behavior
Increasing Interval
Decreasing Interval
Shift Right 5
Shift Down 6
Shift Up 7, left 8
Shift Left 9, Up 10
Stretch of 3
Shrink of 1/2

2. Logarithms and Exponential Transformations

3. Recall… Exponentials and Logarithms are INVERSES!!
What is an inverse???

4. Exponential Transformations
Use what you know about transformation to make conjectures about the following equations with parent function y = 3(2)x. Check your conjectures with your groups and your calculator.
y = 3(2)x y = 3(2)x + 5
y = 3(2)x y = 3(2)x - 5
y = 3(2)x – y = 3(2)x

5. Apply to Logarithms
Use what you know about transformation to make conjectures about the following equations with parent function y = log(x). Check your conjectures with your groups and your calculator.
a. y=log (x + 4) b. y=log (x – 5)
c. y=log (x) – 6 d. y=log (x) + 1
e. y=log (x + 3) – 2 f. y=log (x - 7) + 5

6. A few more… a. y = 3 log(x) b. y = ½ log (x)
Make conjectures about the following transformations with parent function y = log(x). Check your conjectures with your groups and your calculator.
a. y = 3 log(x) b. y = ½ log (x)
c. y = ¼ log(x - 5) d. y = 2log(x) -4

7. Graphing Exponential and Logarithmic Functions!
For all we will be finding:
Transformations
Asymptotes
Domain
Range
End behavior
Increasing intervals
Decreasing intervals

8. Asymptotes Exponential functions: Horizontal Asymptote (H.A.) y=k
Imaginary lines that the graph approaches but never touches
Undefined parts of graph
Determines the shape of the graph when graphing by hand
Exponential functions: Horizontal Asymptote (H.A.)
y=k
Logarithmic Functions: Vertical Asymptote (V.A.)
x=h

9. Logarithmic Examples a. y = log (x) b. y=log (x + 3) – 2
c. y=log (x - 7)+5

10. Exponential Examples
y = 3(2)x
y = 1(4)x +3 -5
y = -2(½)x - 2