Basic Calculus, Continuity of Functions

l. TRUE 0R FALSE Write TRUE if the statement is true otherwise write FALSE 1. One of the conditions a function must satisfy to be continuous at a number is "the value of the limit of f (x) is DNE" 2. A polynomial function is continuous to all real numbers. 3. The function f (x) = x2 2x + 1, continuous to the interval [7,7]. 4. One of the conditions a function must satisfy to be continuous at a number is " f (c) must exist" 5. A function is continuous on a number if and only if f (c) = fim f (x) as x approaches a number C. y 6. The function shown on the graph on the right is continuous at x = . t 5. :15 : 7. The function shown on the graph on the right is continuous at an ' interval of [ 1 , 1] 8. Removable discontinuity is observed at x = 8 on the graph on the . right. i I i -/\ 2 _ I I 0 I E i i 0 I t h + I D I t l i- | I- 9. The function f(x) = x :3: 6 is continuousx = 1. '75 |1 I if 10 15 x 10. If Iim f (x) = DNE, then f (x) is undened at the point x = , ; xya a. II. MULTIPLE CHOICE Write the capital letter of the best answer on the space provide before the number. 1. What is a possible point of discontinuity for the function f (x) = 32::5 ? A. x=5 B. x=-5 C. x=0 D. Undened 2. Which of the following would be a valid reason the function below is non-differentiable at x = 0? A. The graph contains a comer. B. The graph contains a discontinuity. C. The graph contains a cusp. D. The graph contains a vertical tangent. [sum/[72.21 3. Which of the following is NOT a condition related to the continuity of a function f(x)? A. When f (a) is dened C. When limit exists B. When a onesided limit exists D. When f (a) = lim f (x) 4. Classify the function on the right as continuous or classify its discontinuity. A. Continuous B. Discontinuous with a jump discontinuity C. Discontinuous with a removable discontinuity D. Discontinuous with an innite discontinuity Use the graph below for nos. 5 6 _5. Which one of these open intervals is the function discontinuous? A. (-5,-4) B. (-2.0) C. (-4,-2) D. (0,1)