please help with this worksheet

1 of 2 Math 6B-10- Midterm Boost Spring 2020 Name: Instructions Please complete the following problems to the best of your ability. You will earn up to 10 points based on completion and performance which will be added to your total midterm score. You must show work to receive any credit. Submit the completed assignment through Crowdmark no later than Wednesday May 6 at 11:59p. If a limit does not exist or a function is not defined, write DNE. 1. Let n(x) and d(x) be polynomials with no common factors and f(x) = "x. d( x) . Suppose f(x) has all of the following properties: lim f(x) =3 x -00 lim f(x) = 0o lim f(x) = -co x -+-3 f (-1) = 0 lim f(x) = 00 x-+2 lim f(x) = 00 x-+2+ lim f(x) = 3 X -+ 00 i. Draw a "sign chart" for f(x). That is, draw a number line and label the intervals on which f is positive or negative. Remember, a rational function can only change signs at roots of its numerator or denominator. ii. Recall the vertical asymptotes of f correspond with roots of d. Determine the roots of d and whether their multiplicities are even or odd. iii. lim iv. lim = X -+2 v. What is the horizontal asymptote of f? vi. Sketch a graph of f and determine whether its vertical intercept is positive or negative. 2. Suppose g is a quadratic function that has roots at x = -5 and x = 8, and f(0) = 14. Write a function formula for f in factored form in terms of x. 3. Find the vertical asymptotes of f(x) = 3x(x -1)(x + 6)2 x(x - 1)2(x - 9) 4. Let h(x) = =x(12x+7). Compute: i. lim h(x) = x-+00 ii. lim h(x) = iii. lim h(x) = x -+4+ iv. lim h(x) = x-+4 v. lim h(x) = x-+0 5. The graph of the function f is shown below