Download
1 / 11
110 likes | 259 Vues
In this lesson, we delve into the graphing of the natural logarithm function, y = ln(x), and its exponential counterpart, y = e^x. We'll utilize a calculator to visualize their graphs within the specified window and analyze their key properties, including always increasing behavior and one-to-one characteristics. Important key points for y = e^x are shared, and we'll determine corresponding points for y = ln(x). A vertical asymptote at x = 0 is noted, and we’ll highlight unique reflections and comparisons between the two graphs, focusing on the essential characteristics of their inverses.
E N D
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=exand 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
Example Graph: • Where is the vertical asymptote?
Example 2: Graph • First of all, what unique thing will happen with this graph? • There will be a y-axis reflection
Y-axis reflection • Comparison of y=ex and y=e-x • Comparison of y=ln(x) andy=ln(-x)
