Section 2.8 - Continuity. continuous pt. discontinuity at x = 0 inf. discontinuity at x = 1 pt. discontinuity at x = 3 inf. discontinuity at x = -3 continuous.

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Presentation transcript:

Section Continuity

continuous pt. discontinuity at x = 0 inf. discontinuity at x = 1 pt. discontinuity at x = 3 inf. discontinuity at x = -3 continuous jump discontinuity at x = 2

Find the value of a which makes the function below continuous No Calculator

Find (a, b) which makes the function below continuous As we approach x = -1 2 = -a + b As we approach x = 3 -2 = 3a + b No Calculator

A. 2 B. 1 C. 0 D. -1 E. -2

No Calculator Which function is NOT continuous everywhere? undefined at x = -1

Calculator Required Which of the following is true about I. f is continuous at x = 1 II. The graph of f has a vertical asymptote at x = 1 III. The graph of f has a horizontal asymptote at y = 1/2 I. f(1) results in zero in denominator….NO II. Since x – 1 results in 0/0, it is a HOLE, NOT asymptote III. X X X X

The graph of the derivative of a function f is shown below. Which of the following is true about the function f? I. f is increasing on the interval (-2, 1) II. f is continuous at x = 0 III. f has an inflection point at x = -2 A. I B. II C. III D. II, III E. I, II, III NO YES Calculator Required

Let m and b be real numbers and let the function f be defined by: If f is both continuous and differentiable at x = 1, then: If x = 1