II. Setting a Window - Finding One That Works

B. Examples

6. Logarithmic Function Examples

Logarithmic functions will usually have a vertical asymptote, and the domain must be considered.

i) Example 1: Graph the function . There will be a vertical asymptote at x=-3, and the domain is . Therefore, you will not be concerned with values of x less than -3. Consider this when you determine a window. It appears that the graph just stops, but it does not. The reason it has this appearance is because of the pixels.

 Enter the function. Use ZOOM4

ii) Example 2: Graph the function . Since the domain is all real numbers, there is no vertical asymptote and ZOOM6 is a good window.

 Enter the function. Use ZOOM6.

iii) Example 3: Graph the function . To enter this function you must use the Change of Base Formula. There will be a vertical asymptote of x=2. Use TABLE to find values and set the table shown.

 Enter the function. Set the window. Graph the function.

 1. Polynomial 2. Trigonometric 3. Radical 4. Rational 5. Exponential 6. Logarithmic