2. RATIONAL FUNCTIONS Graphing

4. The Rational Parent Function’s Equation and Graph: The Rational Parent Function’s Equation and Graph:. The graph splits into branches by the vertical asymptote(s). These are created when the denominator = 0. We can’t divide by zero! The graph splits into branches by the vertical asymptote(s). These are created when the denominator = 0. We can’t divide by zero!.

5. Vertical Asymptote at x = 1 Horizontal Asymptote at y = 1 Removable Discontinuity At x = -1 x-intercept and y-intercept of 3. No vertical stretch or compression since it’s up 1, over right 1. There has been a POSSIBLE reflection across the x-axis since this branch is below the horizontal asymptote. Let’s Review First….

6. TWO TYPES OF RATIONAL GRAPHS: Method for graphing: Use your knowledge of transformations. Method for graphing: Factor and try to reduce.

7. TRANSFORMATIONAL (SINGLE VARIABLE) Method for graphing: Use your knowledge of transformations. There is a horizontal shift left 4, then a horizontal compression of 3. There is a vertical shift down 7. Since this is 1, no vertical compression or stretch. Transformations in the denominator find the VERTICAL ASYMPTOTE(S). Vertical transformations find the HORIZONTAL ASYMPTOTES. (note: if no shift up or down, the HA is y = 0) This information is useless, unless you are sketching the graph or solving a real life problem.. Let’s look at this graph on the next slide.

9. OTHER RATIONAL: YOU NEED TO FACTOR! Factored: Reduced: Removable Discontinuity (hole) at x = -17 Vertical Asymptote at x = 1 Nothing left in the denominator but a number, so NO Vertical Asymptote. Since the reduced fraction is x – 1, it will look linear, with a hole in the graph at x = -17. Since there are NO x’s in the numerator, but still one in the denominator, the Horizontal Asymptote is y = 0 FACTOR! FACTOR! FACTOR!

11. Let’s look at that graph from before and find an equation. (x + 1) reduces to create the removable discontinuity. (x – 3) creates the x-intercept of 3. The x is there so that both numerator and denominator have equal degrees, to keep the HA y = 1. The -1 was included to make the y-intercept to be 3 (plug in zero for x to check!).

12. RATIONAL FUNCTIONS DONE!