PART I - DO NOT USE A CALCULATOR ON ANY PROBLEM IN THIS SECTION. (Problems 1-37) Consider the graph of function, f, shown below. -10 Answer the following questions about function f. 1.) f(-5) = 2.) f (2) = 3.) f(4) = lim f (x) = lim f (x) = lim f (x) = 4.) x--7 5.) x--5 6.) x-2 lim f (x) = lim f (x) = 7.) x-4 lim f (x) = 0-x (8 9.) x-0 lim f (x) = lim f (x) = lim f (x) = 10.) *-0* 11.) x-4 12.) x-4 lim f (x) = lim f (x) = 13.) *--20 14.) x-+20 15.) Use the definition of a continuous function at a number to answer the following. Be sure to use reasons based on the definition of continuity at a point that we discussed in class. a.) f is not continuous at x = -7 because: b.) f is not continuous at x = 2 because: c.) f is not continuous at x = 4 because:\f28.) Find a c such that J (x ) is 29.) Find the x-values (if any) at which f is 30.) Determine all of the vertical discontinuous. Label as removable or non- asymptotes of f(x): continuous on the entire real line. removable. f (x ) = *+2 when X s4 x 2 - 4 f ( x ) -. f (x) =- 2x+ 6 * 10 when x >4 2x2 -18 31.) True or False: If f is undefined at 33.) The graph of the function f is shown to the right. x = c, then the limit of f(x) as x Which of the following statements is false? approaches c does not exist. a) x = d is in the domain of lim f (x) b) x-a lim f (x) is equal to x-a 32.) True or False: If the lim f (x) = L lim f (x) then f (c ) = L C) x - a exists d) lim f (x ) x - is not equal to f (a) e) J is continuous at X = a lim (x + Ax) - 2(x+ Ax)+1-(x2 -2x+1) 35.) On the graph, draw a function that has the following properties: ) Ar-0 Ax A step (or jump) discontinuity at x = 5 f(5) = 6.Iim 36.] Create a function such that the ""5 does not exist because it is approaching + W from both the left and the right. Show both the function and the graph. 37.] Find a function x) such thatx} has a hole at x = 7 and a vertical asymptote atx = -4