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

Logarithms and Exponential Transformations

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

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. 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

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

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

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

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

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