Aim: What is the continuity? Do Now: Given the graph of f(x) Find 1) f(1) 2) 12 3 4 1 2 3...

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Presentation transcript:

Aim: What is the continuity? Do Now: Given the graph of f(x) Find 1) f(1) 2)

Left-hand limit ≠ right-hand limit, therefore is not exist 6 2 f ( 2 ) DNE

f(x) is continuous at x = a if f(x) is continuous at x = a means i) f(a) must be defined ii) must exist as a finite number Continuous function simply means when draw the graph we don’t need to drop our pen or pencil

. Jump discontinuity. Removable discontinuity

Example: let What value of c will f(x) continuous at x = 1? f(1) is defined 3 = c + 2, c = 1 That means f is continuous at x = 1 only when c = 1

Example: For what values of a and b will f be continuous on R? f(3) is defined

4a – 2b + 3 = 4 9a – 3b + 3 = 6 – a + b 4a – 2b = 1 10a – 4b = 3 -8a + 4b = -2 10a – 4b = 3 2a = 1, a = 1/2 2 – 2b = 1