2. Suppose f(x) is a rational function with leading term -1, has three roots: a root at x = -2 of degree 1, a root at x = 0 of degree 1, and a root at a = 1 of degree 1, f(x) also has a vertical asymptote at x = -1 of degree 3. (a) Determine the sign decomposition of f(x): (b) Graph f(x): (c) (extra credit) Find a rational function with the same properties as f (z).1. In this problem we will give a graph sketch of f(x) _ _ - 4x +4 x2 + 2x a) Factor the numerator and denominator of f(x), find the roots, leading term and asymptotes. X2 - 4 x+4 ( x - 2 . ) 2 x 2+2x x ( x + 2 ) 0 = X 2 - 4 x + 4 * * - 4 x + 4 = 0 X 2 + 2 x ( x - 2) 2 - 0 x - 2 - 0 X = 2 (b) For each root and vertical asymptote from part (a), give the degree. (c) Determine the sign decomposition for f (x) (aka where f (x) is positive and negative). (d) Graph f(x). Include all roots and asymptotes.Problem 1 A right triangle is bounded by the x axis and a circle of raduis 1. Here's a picture to help you visualize: (a) Write y as a function of x. (b) Write the perimeter of the triangle, P, as V a function of the width, x. X (c) Express the area of the triangle, A, as a function of the width, x. Problem 2 Suppose f(x) is a polynomial with degree 4, and has three roots: a root at x = -3 of degree 1, a root at x = 1 of degree 2 and a root at x - 3 of degree 1. If f(0) = 3, we aim to give a graph sketch of f (x). (a) Determine the sign decomposition of f (x): (b) Graph f(x):Problem 3 In this problem we will give a graph sketch of f(x) = (3 - x)(x + 2)(x - 1). (a) Factor f(x), find the roots. (b) For each root from part (a), give the degree. (c) Determine the sign decomposition for f(x). (d) Graph f(x)