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.

f(x) = 1/x^2-4 (x-2)(x+2)

end behavior x -> ∞ y = 0 x -> ∞ y = 0

asymptote x -> -2- y -> ∞ x -> -2+ y -> - ∞ x -> +2- y -> - ∞ x -> +2+ y -> ∞

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, zeros of the denominator --> x = -1 and 1 which are under the numerator meaning they are vertical asymptotes of the f(x)

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 intercept by the horizontal and vertical asymptotes. The graph would be shifted left ax=-b and down cx=-d. The y intercept would be b/d. For the x intercept you would cross multiply so the denominator disappears, and 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.

f(x) = (-3x^2-10) / (x+5) (x-2)