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=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))

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

Graph comparison

Example Graph:

•Where is the vertical asymptote?

Answer

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

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

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

Example 2 Continued