11
Lesson 35: y=ln(x)

Lesson 35: y= ln (x)

Embed Size (px)

DESCRIPTION

Lesson 35: y= ln (x). Warm Up Preview:. Graph the following on calc…. Use the window x[-1,2] and y [0,5] Notices the relative position of each graph Less than zero, at zero, greater than zero. Properties of y=e x and its inverse. Always increasing One to one (inverse exists) - PowerPoint PPT Presentation

Citation preview

Page 1: Lesson 35: y= ln (x)

Lesson 35: y=ln(x)

Page 2: Lesson 35: y= ln (x)

Warm Up Preview:

Page 3: Lesson 35: y= ln (x)

Graph the following on calc….

•Use the window x[-1,2] and y [0,5]

•Notices the relative position of each graph▫Less than zero, at zero, greater than zero

Page 4: Lesson 35: y= ln (x)

Properties of y=ex and its inverse•Always increasing•One to one (inverse exists)•Inverse of y=ex defined as y=ln(x)

▫ .•Key points of y=ex are (0,1), (1, e), (2, e2)

▫What would the key points of y=ln(x) be? •Use the domain and range of y=ex to find

the domain and range for its inverse (y=ln(x))

Page 5: Lesson 35: y= ln (x)

Graphing y=ln(x)

•Graph of ln(x) is constantly increasing and concave down.

•Let’s compare the graphs for y=ex and y=ln(x)▫Use the 3 key points to graph each

•Vertical Asymptote at x=0

Page 6: Lesson 35: y= ln (x)

Graph comparison

Page 7: Lesson 35: y= ln (x)

Example Graph:

•Where is the vertical asymptote?

Page 8: Lesson 35: y= ln (x)

Answer

Page 9: Lesson 35: y= ln (x)

Example 2: Graph•First of all, what unique thing will happen

with this graph? •There will be a y-axis reflection

Page 10: Lesson 35: y= ln (x)

Y-axis reflectionComparison of y=ex and y=e-x Comparison of y=ln(x) andy=ln(-x)

Page 11: Lesson 35: y= ln (x)

Example 2 Continued