1. Daily Warm-Up Quiz 1.Describe two ways to graph the inverse of a logarithmic function. 2.Name at least three features of the graph of a logarithmic function. 3.Describe the procedure for writing the inverse of an exponential function. You may examples in your description. Mrs. McConaughyHonors Algebra 21

2. Short, Short Summary of Translations in Basic Graphs Before reviewing last night’s homework, recall: Y 1 = │ x-3 │ + 2 Y 2 = (x-3) 2 + 2 Y 3 = 2 x-3 + 2 Y 4 = log 2 (x-3) + 2 Mrs. McConaughyHonors Algebra 22

3. Mrs. McConaughyHonors Algebra 23 Technology Connection: Graphing Logarithmic Functions and Their Inverses During this mini-lesson, you will use a graphing utility to:  Graph logarithmic functions using change-of-base formula  Graph the inverse of a logarithmic function  Graph the inverse of an exponential function

4. Mrs. McConaughyHonors Algebra 24 EXAMPLE: Graphing Logarithmic Functions We can use the change-of-base formula to graph logarithmic functions with bases other than 10 or e (read “natural base e”) on a graphing utility.

5. Mrs. McConaughyHonors Algebra 25 Graph y = log 2 x and y = log 20 x in the same viewing rectangle. Solution: Step 1: Rewrite each function using change-of- base formula: log 2 x = ln x and log 20 x = ln x ln 2 ln 20 EXAMPLE: Graphing Logarithmic Functions

6. Mrs. McConaughyHonors Algebra 26 EXAMPLE: Graphing Logarithmic Functions Step 2: Enter each function as: y 1 = ln (x) ÷ ln (2) ENTER Y 2 = ln (x) ÷ ln (20) ENTER * Use a [ 0, 10, 1] x [-3, 3, 1] viewing rectangle. y = log 2 x y = log 20 x

7. Mrs. McConaughyHonors Algebra 27 Checking for Understanding Now graph y = log 3 x and y = log 15 x. y = log 3 x y = log 15 x

8. Mrs. McConaughyHonors Algebra 28 Checking for Understanding y = log 3 x Y = log 3 (x + 2) Y = 2 +log 3 x Describe the change(s) that need to be made to the graph of y = log 3 x to obtain each of these three graphs. Now, graph y 1 = log 3 x using a graphing utility (and the change-of-base formula). Next, graph y 2 = 2 + log 3 x and y 3 = log 3 (x + 2) in the same viewing rectangle as y = log 3 x.

9. Mrs. McConaughyHonors Algebra 29 Inverse of an Exponential Function By definition, f(x) = a x and g(x) = log a x are inverses of each other. NOTE: You can use this definition to easily graph the inverse of a number of exponential or logarithmic functions using a graphics calculator.

10. Mrs. McConaughyHonors Algebra 210 Match each function with the graph of its inverse: f (x) = log 3 x g (x) = log ½ x h (x) = log 2 4x f -1 = 3 x g -1 = (1/2) x h -1 = ____ 1. Switch x and y. 2. Rewrite in exponential form. 3. Graph in y = form. f -1 = 3 x g -1 = (1/2) x h -1 = ___

11. Mrs. McConaughyHonors Algebra 211 Final Check for Understanding Describe the steps needed to graph the inverse of the exponential function y = 2 x. Use any convenient method. Solution: Step 1: Rewrite in exponential form y = log 2 x. Step 2: Use change-of-base formula to graph.

12. Final Checks for Understanding 1.In each problem below, compare the graph of h(x) with the graph of f(x). Note: You will first need to describe f(x). a. f(x) = log 2 x ; h(x) = log 2 (x-1) + 3 b. f(x) = 2 x ; h(x) = 2 x+ 1 – 3 2.Explain how to set the “standard viewing window” on your graphing calculator. Do this, then write the dimensions. How can you alter these dimensions? 3.To graph a logarithmic function, you must first graph _________________. Once you have done this, you can use the following two methods to graph the logarithmic function: ___________ or _________ Mrs. McConaughyHonors Algebra 212

13. Mrs. McConaughyHonors Algebra 213 Homework Assignment: Study for 8.1 -8.3 Weekly Quiz