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Unformatted text preview: c Kendra Kilmer January 11, 2012 Section 2.4  Continuity
Deﬁnition: A function f is continuous at the point x = a if all of the following are true:
1.
2.
3.
Note: If one or more of the conditions are not met, we say f is discontinuous at x = a.
Example 1: For what values of x is the function discontinuous? Explain. 6
5
4
3 f(x) 2
1
−6 −5 −4 −3 −2 −1 123
−1
−2
−3
−4
−5
−6 4 56 Deﬁnition: A function f is continuous from the right at a number a if and f is continuous from the left at a if Deﬁnition: A function is continuous on an interval if it is continuous at each point on the interval.
10 c Kendra Kilmer January 11, 2012 The following types of functions are continuous at every number in their domains: If f and g are continuous at a and c is a constant, then the following functions are also continuous at a: If g is continuous at a and f is continous at g(a), then Example 2: Find the intervals on which the following functions are continuous.
a) f (x) = 3x9 + 4x5 − 7 b) g(x) = 23x + 4 c) h(x) = log8 (x − 3) − 2 d) k(x) = x+2
x2 − 3x − 10 x − 5 x + 2
e) m(x) = 2x2
x x−4 if x ≤ −3
if − 3 < x ≤ 0
if x > 0 11 c Kendra Kilmer January 11, 2012 Example 3: Find the value(s) of k that make f (x) continuous everywhere.
f (x) = 2x − 5
x2 + k if x ≤ 1
if x > 1 Section 2.4 Highly Suggested Homework Problems: 3, 5, 11, 15, 17, 19, 29, 31, 33, 35 12 ...
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 Fall '08
 Allen
 Continuity

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