Please answer the following correctly and show your work.

Name: Student ID: If the statement is true, write "T" in the box on the right, otherwise provide an example for which the statement is false. lim f (x) (f) lim J (3) Answer: x -a g(x) lim g(x) (g) If lim f(x) = a, then f(x) has a vertical asymptote at x = a. Answer: (h) If f(x) is not defined at x = a, then lim f(x) = 00 or - 0. Answer: (i) If a function has the following values, then it has exactly 3 roots in the interval [2, 5]. f (2) = -1, f(3) = 1, f(4) = -1, f(5) = 1 Answer: (j) If f(x) = x2 + 3x - 1 then Answer: a f(x) = lim - x + 2xh + h2+ 3x+3h- 1 h 24. Create a function that has the graph below as its graph. Clearly identify how your function has the features shown in the graph (ie., roots, asymptotes, long-term behaviour, etc.) [5: 1 for the function, 4 for justifying] -5 5 10 5