1. Warm-up
Without a calculator, state all of the following: 1) y=-3(x + 4)2 - 5 a) Transformations b) Domain c) Range

3. Logarithms and Exponential Transformations and Inequalities

4. Transformation Review
Describe the transformation for the following quadratic equations with parent function y = x2.
y = (x + 4)2 + 1
y = –x2 – 4
y = 2(x – 1)2 + 5
y = -3(x – 5)2

5. 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

6. 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. log (x + 4) b. log (x – 5)
c. log (x) – 6 d. log (x) + 1
e. log (x + 3) – 2 f. log (x - 7) + 5

7. 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
Do the graphs look like you expected? Explain why or why not.

8. Some Domain and Range Review

9. Domain and Range of Logarithms
Graph the function y = log x in your calculator. Using the graph and your knowledge of asymptotes, find the following:
Domain:
x > 0
Range:
All real numbers

10. Transformed Domain and Range:
Find the domain and range for the following:
a. log (x + 4) b. log (x – 5)
D: {x > -4), R: {all real}
c. log (x) – 6 d. log (x) + 1
D: {x > 0), R: {all real}
e. log (x + 3) – f. log (x - 7) + 5
D: {x > -3), R: {all real}
D: {x > 5), R: {all real}
D: {x > 0), R: {all real}
D: {x > 7), R: {all real}

11. Domain and Range of Exponentials
Find the domain and range for the following exponential equations.
y = 3(2)x y = 1(4)x +3 -5
y = 2(3)x y = 4(2)x
y = -2(½)x y = 1(.75)x-4 +3