Continuity of A Function

A function f(x) is continuous at x = c if and only if all three of the following tests hold: f(x) is right continuous at x = -5 f(x) is continuous at x = -4 f(x) has infinite discontinuity at x = -3 [i, iii] f(x) has point discontinuity at x = -2 [i, iii] f(x) has infinite discontinuity at x = -1 [i, ii, iii] f(x) is continuous at x = 0

At x = 1 At x = 2 At x = 3 At x = 4 At x = 5 Point Discontinuity [i, iii] Jump Discontinuity [i, ii, iii] Continuous Point Discontinuity [i, (ii), iii]

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

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

Consider the function Find the value of k which makes f(x) continuous at x = 0 Since, if k =1, the hole is filled.

Continuity of a Composite Function If f is continuous at c, and if g is continuous at f(c ) is continuous at c. Since f is continuous at all c, and since g is continuous at all f(c ), is continuous

Since f is continuous at all c, and since g is discontinuous at all f(c ) < 0, is discontinuous at x – 1 < 0 is discontinuous at x < 1