The questions are in the image below. There are EIGHT (8) questions including the bonus question. please attach only the work and info used. Thank you in advance.

Rational Functions Assignment Full credit will only be given for complete solutions. Please sketch all graphs with a ruler. 1/ State the domain, horizontal asymptote, vertical asymptotes, positive and negative intervals, and increasing and decreasing intervals for the reciprocal function y = F(x) 1 if f (x ) = x2 - 4. 2/ If f (x) = =2x+3 x+4 , -, determine the behaviour at the vertical asymptote using 'approach' tables. 3/ Create a possible equation for the rational function that satisfies the conditions: an x-intercept at x = -2, vertical asymptotes at x = -1 and x = 3, and an oblique asymptote at y = Q(x). 4/ Create a possible equation for the rational function that satisfies the conditions: g (3) = 0, h(3) = 0, a vertical asymptote at x = 3, and a removable discontinuity [i.e., a hole] at (1, }). 5/ Determine a possible equation for the rational function given the graph below. 6/ Complete the "curve sketching algorithm" for f (x) = 2 23 - 8 * 2 + 3 x + 2 ' . Sketch the graph. 7/ Complete the "curve sketching algorithm" for f (x) = x 3 - 1 x3 -3x2+2x . Sketch the graph. BONUS PROBLEM/ If T = x2 + , determine the values of b and c so that x + = T3 + bT + c for all non-zero real numbers, x