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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
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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