Class Opener:

http://sbstjohn.com/QODWebSite/IntermedAlg/inter_1213_f023.htm

http://sbstjohn.com/QODWebSite/PreElemAlg/alg_1213_f168.htm

Review of Yesterday:

• Look at problem 40 in text.

Guidelines for Graphing Rational Functions

1. Simplify f, if possible. Any restrictions on the domain of f not in the simplified function should be listed.

2. Find and plot the y intercept (if any) by evaluating f(0).

3. Find the zeros of the numerator (if any) by setting the numerator equal to zero. Then plot the corresponding x intercepts.

Guidelines for Graphing Rational Functions

4. Find the zeros of the denominator (if any) by setting the denominator equal to zero. Then sketch the corresponding vertical asymptotes using dashed vertical lines and plot the corresponding holes using open circles.

5. Find and sketch any other asymptotes of the graph using dashed lines.

Guidelines for Graphing Rational Functions

6. Plot at least one point between and one point beyond each x-intercept and vertical asymptote.

7. Use smooth curves to complete the graph between and beyond the vertical asymptotes, excluding any points where f is not defined.

Sketching the Graph of a Rational Function:

• Sketch the graph of:

Example 2:

• Sketch the graph of:

Example 3:

• Sketch the graph of:

Example 4:

• Sketch the graph of:

Example 5:

• Sketch the graph of:

Example 6:

• Sketch the graph of:

Slant Asymptote:

• If the degree of the numerator is exactly one more than the degree of the denominator , the graph of the function has a slant ( or oblique) asymptote.

• For us to find the equation of a slant asymptote we use long division.

Example:

• Find the equation of the slant asymptote for:

Sketch the Graph

• Sketch the graph of:

Student Check:

• Sketch the graph of the following function:

Application:

• A rectangular page is designed to contain 48 square inches of print. The margins on each side of the page are 1.5 inches wide. The margins at the top and bottom of the page are each 1 inch deep. What should the dimensions of the page be so that the minimum amount of paper is used?

Student Check:

• A rectangular page is designed to contain 57 square inches of print. The margins on each side, as well as the top and bottom, are all 1 inch deep. What should the dimensions of the page be so that the least amount of paper is used.

Practice:

•Pg. 162 – 163 •#77 – 86