5.3 Properties of Rational Functions Additional Homework Problems 1. Graph the function using transformations. Describe the transformations. Label at least two points on the graph and any asymptotes. a. f (x) =- x+3 2 b. g (x) =- + 3 (x +1) 2. For the following functions. a. State the domain. Use set-builder notation or interval notation. b. State the vertical and horizontal asymptotes, if any. a. f (xx) = - 5x x +3 b. f (x) =- x-5 x2 -3x -4 c. f (x) =- x+x-6 x3 + 8x +15 3. Write a rational function with a Vertical Asymptote of x =7 and a Horizontal Asymptote of y =3. 4. Write a rational function with 2 Vertical Asymptotes and a Horizontal Asymptote of ) =0 .5.4 Graphing Rational Functions 1. Homework Problems Graph each function- Include intercepts, asymptotes, and holes, if any. a. State the domain. Use setbuilder notation or interval notation. b. In each graph, include intercepts, asymptotes, and holes, if any. Write asymptotes as lines 1: = _ or v = graph. 1+4 and include them as dashed lines on the 2. Write the rational function corresponding to the given graph. Explain your reasoning. Note: the VA is at x = 5 ' 1 13 I 15 1 I 12 I I 6 912151321 ab _______ 3. Write the rational function corresponding to the given graph. Explain your reasoning. b. Use the graph of the function f to solve the inequality. (a) f(x) 0, where R(x) = by using the graph of the function. The solution set for R(x) > 0 is x(x - 5) (Type your answer in interval notation.) 2-1 X 2 4 6 y8= X 0 X =5Solve the following inequality. (x1)(x5}(x6)50 On your paper: graph the corresponding polynomial function to help you solve the inequality. The solution is E (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) Solve the Inequality x35x224x>0 On your paper graph the corresponding polynomial function to help you solve the inequality. The solution is . (Simplify your answer, Type your answer In Interval notation Use integers or fractions for any numbers in the expression) Solve the inequality. x+5 xQ s0 On your paper. graph the appropriate rational function. Then use the graph to solve the inequality. The solution is D. (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)