Unit+4+Virtual+Notebook

__**Unit 4 Lesson 2**__

1. Create a rational function whose vertical asymptotes add to zero and whose zeros add to zero. Describe the asymptote behavior and end behavior of the function you created using limit notation. Asymptote Behavior: x -> (-2-) y -> ∞ x -> (-2+) y -> - ∞ x -> (+2-) y -> - ∞ x -> (+2+) y -> ∞ End Behavior: x -> ( ∞ ) y ->0 x -> ( ∞ ) y ->0 2. True or false: A rational function as a vertical asymptote at x = c every time c is a zero of the denominator. If the statement is false justify your answer using mathematical terminology learned in class and examples of at least 2 functions that make this statement false. True 3. Describe how the graph of a nonzero rational function f(x) = (ax+b)/(cx+d) can be obtained from the graph y = 1/x. **You can determine the y and x intercepts, the vertical and horizontal asymptotes. The graph is shifted left ax = -b units and down cx = -d units. the y intercept should be easy to find, since it is just b/d. as for the x intercepts, you do cross multiply, in which the denominator disappears, and you solve 0 = ax + b.** 4. Write a rational function with the following properties: (a) Vertical asymptotes: x = -5 and x = 2. (b) Horizontal asymptote: y = -3. (c) //y//-intercept 1. All Three