please WRITE NEATLY!! SHOW YOUR WORK!!! AND CIRCLE ALL YOUR ANSWERS!

x23x+2 x32x2 1. Given: f(x) = Re-write the function by factoring numerator and denominator completely. f(x) = Reduce common factors. Identify the xvalue of the hole in the graph. Now. examine the reduced expression. For what value of x does the function have a vertical asymptote? . 6 _ d] Sketch the graph, indicating the hole and the .f . . vertical asymptote. : . I. e] Describe the behavior of the graph as x g) 11] approaches the vertical asymptote from both the left - -2 - and right sides? in (n. I 2:. 9'4 .L. 0-1 N. 4*]. IL U11 6- i: What is the limit of [[x} as x approaches the vertical asymptote? Evaluate the reduced expression at the value of x which corresponds with the hole in the graph. What is the limit of x] as x approaches the hole? x1 2. Given: f(x) = m a] What is the conjugate of the denominator? b] Multiply numerator and denominator by the conjugate, and simplify your results. c) There is a common factor in the numerator and denominator. Reduce the fraction and identify the x-value of the hole in the graph. d] What is the limit of the function as x approaches the hole in the graph? 3. Given f (x) = 1 X x2+x a) Re-write the function as a single fraction. (find the common denominator and combine the fractions) Simplify your answer. b) Find lim f(x) X--1 c) Find lim f (x) x-0 d) At which value of x is there a removeable discontinuity? Why?4. Use an algebraic method (factoring, rationalizing, or combining fractions) to evaluate each limit. a) lim Vx-v5 x-5 x-5 b) lim- 2x2-3x-2 x-2 5x2-10x c) lim 2 10 x-10 x-10