Continuity of a function

thejadekid

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May 1, 2020
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Hi can someone help me clarify the answer for letter D? I’m confused whether it’s continuous or discontinous. Thanks

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Can you tell us what confuses you about it? It's easier to clarify something when you see what unclarity needs to be removed.

Were you given a definition for "continuous on an open interval"? What is it?
 
Since both 2x-1 and x^2 are polynomials (a line is both linear and polynomial) they are continuous on their domain. The problem is do they link up nicely. That is, is f(x) continuous at x=1.

f(x) is continuous at x=1 if the following conditions are met:
1a) The left hand limit at x=1 exist
1b) The right hand limit at x=1 exist.
2) Both of the limits in 1 are equal. Say the common limit is L
3) f(1) = L

Have all these conditions been met in your example. If not, then the function f(x) is not continuous at x=1. Which conditions, if any, have not been met??
 
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