Consider the following graph of the function g. -2 O 2 For which value(s) of a does g(x) approach a different number from the right side than it approaches from the left side? (Select all that apply.) 0 -3 0 -2 10 -1 0 1 0 3 X For which value(s) of a does g(x) increase or decrease without bound as x approaches a or for which value(s) of a is g(x) not defined? (Select all that apply.) 0 -3 0 -2 0 -1 0 1 0 3-2 For which value(s) of a does g(x) approach a different number from the right side than it approaches from the left side? (Select all that apply.) -3 0 -2 0 -1 0 1 0 3 X For which value(s) of a does g(x) increase or decrease without bound as x approaches a or for which value(s) of a is g(x) not defined? (Select all that apply.) -3 0 -2 10 -1 0 1 0 3 X From the given graph of g, state the numbers at which g is discontinuous. (Enter your answers as a comma-separated list. ) X =The graph of a function f is given. (Enter your answers as comma-separated lists.) YA X (a) At what numbers a does lim f(x) not exist? x- a a = X (b) At what numbers a is f not continuous? a = (c) At what numbers a does lim f(x) exist but f is not continuous at a? x - a a =The toll T charged for driving on a certain stretch of a toll road is $1 except during rush hours (between 7 a.m. and 10 a.m. and between 4 p.m. and 7 p.m. ) when the toll is $3. (a) Sketch a graph of T as a function of the time t, measured in hours past midnight. 3 3 3 . 1 7 t 10 16 19 24 7 10 16 19 24 7 10 16 O 19 24 i 39 -O 1 .o -o 7 10 16 19 24(b) Discuss the discontinuities of of this function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) t=|DNE X Classify the discontinuities as removable, jump, or infinite. O removable O jump O infinite O none T is continuous Discuss the significance of the discontinuities of this function to someone who uses the road. O The function is continuous, so there is no significance. O Because of the sudden jumps in the toll, drivers may want to avoid the higher rates between t = 7 and t = 10 and between t = 16 and t = 19 if feasible. O Because of the sudden jumps in the toll, drivers may want to avoid the higher rates between t = 0 and t = 7, between t = 10 and t = 16, and between t = 19 and t = 24 if feasible. O Because of the steady increases and decreases in the toll, drivers may want to avoid the highest rates at t = 7 and t = 24 if feasible. Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. p(v) = 6\\ 7v2+ 2, a=1 V - 1 lim p(v) = lim 6\\/ 7v2+ 2 V - 1 = 6 lim v 7v2+ 2 V - 1 by the ---Select--- = 6 lim 7v2 + 2) V - 1 by the ---Select--- = 61 lim V - 1 (7v2 + lim 2 by the ---Select--- V - 1 = 61 7 lim V2 V - 1 + lim 2 by the ---Select--- V V - 1 = 6V7 . (1) + 2 by the ---Select--- V Find p(1). p(1) = Thus, by the definition of continuity, p is continuous at a = 1