2. Objective Video Example by Mrs. G Give It a Try Lesson 9.3  Graph rational function that cannot be written in transformational form.

3. Video Objective Video Example by Mrs. G Give It a Try

4. Example by Mrs. G Objective Video Example by Mrs. G Give It a Try Click to continue. Steps for graphing rational functions: Step 1: Find the vertical asymptotes. Vertical asymptotes occur at the values of x that make the denominator zero. Set the denominator equal to zero and solve.

5. Example by Mrs. G Objective Video Example by Mrs. G Give It a Try Click to continue. Steps for graphing rational functions: Step 2: Find the end behavior asymptotes. End behavior asymptotes can be horizontal or “slant” Compare the “bigness” of the numerator and denominator. One of three things with happen. If degree of denominator is larger than degree of numerator, then horizontal asymptote at y = 0. If degree of denominator is equal to degree of numerator, then horizontal asymptote at y = (leading coefficient of num.)/(leading coefficient of den.) If degree of denominator is smaller than degree of numerator, then slant asymptote at y = (quotient of polynomials)

6. Example by Mrs. G Objective Video Example by Mrs. G Give It a Try Click to continue. Steps for graphing rational functions: Step 3: Find the x - intercepts. x – intercepts occur when y = 0 y = 0 in a rational function when the numerator equals 0 Therefore, set the numerator equal to 0 and solve for x.

7. Example by Mrs. G Objective Video Example by Mrs. G Give It a Try Click to continue. Steps for graphing rational functions: Step 4: Find the y - intercepts. y – intercepts occur when x = 0 Substitute 0 for all x in the expression and evaluate When x = 0, y = (constant of numerator)/(constant of denominator)

8. Example by Mrs. G Objective Video Example by Mrs. G Give It a Try Click to continue. Steps for graphing rational functions: Step 5: Prepare to graph Choose an appropriate scale based on the results of steps 1 – 4. Draw in the vertical and end behavior asymptotes. Plot the x – and y – intercepts.

9. Example by Mrs. G Objective Video Example by Mrs. G Give It a Try Click to continue. Steps for graphing rational functions: Step 6: Graph Make a table of values. Choose x values that will help to “complete the picture” of your graph. Plot the points from the table of values. Sketch the curves of your graph.

10. Give It a Try Objective Video Example by Mrs. G Give It a Try Bring your work and answer to our next class! For the function try to find the necessary information from as many steps as you can. DO NOT GRAPH. We will do that together next class.