Homework Help: Calculus

Posted by Abigail on Monday, February 7, 2011 at 12:51pm.

A function f(x) is said to have a removable discontinuity at x=a if:
1. f is either not defined or not continuous at x=a.
2. f(a) could either be defined or redefined so that the new function IS continuous at x=a.

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Let f(x)=x^2+ 14x +51 if x is less than -7
f(x)= 1 if x=-7
f(x) = −x^2−14x−47 if x is greater than -7

Show that f(x) has a removable discontinuity at x=−7 and determine what value for f(−7) would make f(x) continuous at x=−7.
Must redefine f(−7)=.
Now for fun, try to graph f(x). It's just a couple of parabolas

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