UNIT 1.4 & 1.5

Answer these questions on paper (drawn/written), please:

UNIT 1.4:

\fEach function in Exercises 9-12 is discontinuous at some value X = c. Describe the type of discontinuity and any one-sided continuity at x = , and sketch a possible graph of f. 8. Given the following function f, define f (1) so that f is con- tinuous at x = 1, if possible: f (x) = 3x - 1, ifx 1.For each function f graphed in Exercises 23-26, describe the intervals on which f is continuous. For each discontinuity of f, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements. \fSketch the graph of a function f described in Exercises 27-32, if possible. If it is not possible, explain why not. \fIn Exercises 3944, use Theorem 1.16 and left and right lim- e to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity. \fUse the Intermediate Value Theorem to show that for each function f, interval [a,b], and value K in Exercises 55- 60, there is some (a,b) for which f(c) = K. Then use a graphing utility to approximate all such values . You may assume that these functions are continuous everywhere. 55. f(x) = 5 - x4, [a, b] = [0, 2], K = 0\f\f\f\fx2 + 1, ifx 0Use the Squeeze Theorem to find each of the limits in Exer- cises 79-86. Explain exactly how the Squeeze Theorem applies in each case. \f\f