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

Logarithms and Exponential Transformations and Inequalities

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

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-5 y = 3(2)x + 5 y = 3(2)x +6 y = 3(2)x - 5 y = 3(2)x – 8 - 4 y = 3(2)x + 3 + 3

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

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.

Some Domain and Range Review

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

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) – 2 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}

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 + 4 y = 4(2)x y = -2(½)x - 2 y = 1(.75)x-4 +3