Question

answer all with clear handwriting please.

2. (4 points) Let f(x) = x - 9x - 36x”. Find the zeros of the function algehraically (by factoring). and give the exact multiplicity for each zero (not just odd/even). State the behavior of the graph at each zero (whether the graph crosses the x-axts or touches the x-axts and turns around at each zero). Zero Multiplicity Behavior 3. (4 points) Solve the following inequality and graph the solution set on a Real Number Line. Be sure to show your boundary point(s), number line, and test value work. Express the solution set in interval notation. xl-5x2 - 4x + 20 S 0 4 (6 points) Consider the rational function R(x) (a) Factor the function completely and simplify if possible. (b) Answer the following questions based on your work in part a Will there be any vertical asymptotes? If yes, find the equation of the vertical asymptotes, (c) Will there be any holes in the graph of the function? If yes, state the x-coordinate of the hole (d) Will there be any horizontal asymptotes? If yes, find the equation of the horizontal asymptote

Answer 1

Graph of problem (2)

(2). fox)= x4_9x²_36a2 aux-94-36 ) =0 xo u having melipicity 9781-4 (-36) 2 U= x²-90-36 a 12x+3x-36-0 2 9+ 81+144 9 € 25 q+15 x(x-12 ) + 3(x+2) =0 62+3)(x+2) = 0 2 2 2 = 29 3 20 x = -6 2 = 12, X-3 2- x= 12, Behaviour Zuo Mutiplicly x=0 2 x = 12 thie yaxis a=-3 line paralled to axis at a doslance 82 the line paralled to you axes at destance-3 - 5x2_40+20 co (3) 3 X - 4 20 -5 2 2 -6 zo -3 -10 Lo - ak32-10-0 31 V9+40 - 37 h 2 z = = 5,02 (x+2)(1-2)(3-5) $20 (-2,-2), 6-0,2), (-0,5)

I could not answer problem 4 it comes under different area

5 9 5. -15 -10 -5 5 10 15.