math problem

 9. Given the polynomial f(x) = (x – 2)^2 (x + 8)^4 (x + 4)^3 

a. Find the zeros of the expression, and their multiplicities 

b. At each zero, determine whether the graph crosses the x-axis, or merely touches the x-axis and bounces off 

c. Find the maximum number of turning points 

d. Find the power function, and use it to characterize the function’s end behavior  

9. Given the rational function f(x) = 5x^2/ 4x^2 + 8x + 4 (this is in fraction form)

a. Find the horizontal asymptote. If a horizontal asymptote does not exist, explain why. 

b. Find the oblique asymptote. If an oblique asymptote does not exist, explain why. 

c. Find the vertical asymptote(s). If a vertical asymptote does not exist, explain why