December 15 No starter today. Get out a piece of paper and write down the following objectives and examples. Then, solve the examples. Content Objective: SWBAT identify asymptotes, holes, and intercepts of rational functions. Language Objective: SWBAT describe what horizontal and vertical asymptotes are. Draw the graph. Write the equation when is shifted up 1, left 4, and reflected over the x-axis.

If a function has a polynomial in the denominator, the graph of that function will have a gap wherever the denominator is zero (0). If there is no value for x that makes the denominator zero (0), it is a continuous graph. x≠ -2 x≠2 If there is a value for x that makes the denominator zero (0), it is a DIScontinuous graph.

If a function has a polynomial in the denominator, the graph of that function will have a gap wherever the denominator is zero (0). x≠ -2 x≠2 A removable discontinuity is called a hole. A non-removable discontinuity is a vertical asymptote.

A list of items to find on a Rational Equation Vertical Asymptotes: What makes the denominator zero (0) AND CANNOT be simplified? Holes: What makes the denominator zero (0) AND CAN be simplified? X-intercepts: What makes the numerator zero (0)? *After the function is simplified Domain: Everywhere the graph has an x-coordinate. Y-intercepts: Plug zero (0) in for x and solve.

A list of items to find on a Rational Equation, cont. Horizontal Asymptotes: If the degree of the numerator is less than the degree of the denominator, the asymptote is y=0 If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote If the degree of the numerator and denominator are the same, the horizontal asymptote is the lead coefficient of the numerator over the lead coefficient of the denominator Example: For it is

For the following equations, find: Vertical Asymptotes: Holes: Horizontal Asymptotes: X-intercepts: Domain: Y-intercept:

For the following equations, find: Vertical Asymptotes: Holes: Horizontal Asymptotes: X-intercepts: Domain: Y-intercept:

For the following equations, find: Vertical Asymptotes: Holes: Horizontal Asymptotes: X-intercepts: Domain: Y-intercept:

The LAB Writing is incorporated into the assignment. Section 3.6, No. 1-6, 14-19, 22-25, 28, 34 The LAB Writing is incorporated into the assignment.