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. McConaughy Honors Algebra 2 1

Short, Short Summary of Translations in Basic GraphsBefore reviewing last night’s homework, recall:Y1 = │x-3│+ 2

Y2 = (x-3)2 + 2

Y3 = 2x-3 + 2

Y4 = log2 (x-3) + 2

Mrs. McConaughy Honors Algebra 2 2

Mrs. McConaughy Honors Algebra 2 3

Technology Connection: Graphing Logarithmic

Functionsand 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

Mrs. McConaughy Honors Algebra 2 4

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.

Mrs. McConaughy Honors Algebra 2 5

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

Mrs. McConaughy Honors Algebra 2 6

EXAMPLE: Graphing Logarithmic Functions

Step 2: Enter each function as:

y1 = ln (x) ÷ ln (2) ENTER

Y2 = ln (x) ÷ ln (20) ENTER

* Use a [ 0, 10, 1] x [-3, 3, 1] viewing rectangle.

y = log2x

y = log20x

Mrs. McConaughy Honors Algebra 2 7

Checking for Understanding

Now graph y = log3x and y = log15x.

y = log3x

y = log15x

Mrs. McConaughy Honors Algebra 2 8

Checking for Understanding

y = log3xY = log 3 (x + 2)

Y = 2 +log 3 x

Describe the change(s) that needto be made to the graph of

y = log3x to obtain each of thesethree graphs.

Now, graph y1 = log3x

using a graphing utility (and the change-of-base formula).

Next, graph y2 = 2 +

log3x and y3 = log3 (x + 2) in the same viewing rectangle as y = log3x.

Mrs. McConaughy Honors Algebra 2 9

Inverse of an ExponentialFunction

By definition, f(x) = ax and g(x) = loga x are inverses of each other.

NOTE: You can use this definition to easily graph theinverse of a number of exponential or

logarithmic functions using a graphics calculator.

Mrs. McConaughy Honors Algebra 2 10

Match each function with the graph of its inverse:

f (x) = log 3x g (x) = log½x

h (x) = log 24x

f-1 = 3xg-1 = (1/2)x h-1 = ____

1. Switch x and y.2. Rewrite in exponential form.

3. Graph in y = form.

f-1 = 3x g-1 = (1/2)x h-1 = ___

Mrs. McConaughy Honors Algebra 2 11

Final Check for Understanding

Describe the steps needed to graph the inverse of the exponential function

y = 2x. Use any convenient method. Solution:

Step 1: Rewrite in exponential form y = log2x.

Step 2: Use change-of-base formula to graph.

Final Checks for Understanding1. 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) = log2 x ; h(x) = log2 (x-1) + 3

b. f(x) = 2x ; h(x) = 2x+ 1 – 32. 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. McConaughy Honors Algebra 2 12

Mrs. McConaughy Honors Algebra 2 13

Homework Assignment:

Study for 8.1 -8.3 Weekly Quiz