The problem i was given something like this -
f(X) =
{x^2 + 3, x > 1
ax^2 + bx2, x < 1}
^that being a piecewise function.
That's not exactly what the problem was, but the important parts are still preserved. Now the question was "At which values of a and b is the function continuous?"
Naturally, my response is, "x is never equal to 1, therefore the function can never be continuous, regardless of the values of a and b."
Now, in my definition that I was given for "continuous function", it went something like the dictionary definition ofObviously it has a break. But she tells meQuote:
Of or relating to a line or curve that extends without a break or irregularity.
and I respond with my above arguement, so she tells meQuote:
But the function is continuous elsewhere
Well, i still completely disagree, can anyone tell me why I am wrong?Quote:
just because the function doesnt specify a value at x =1 , doesnt mean that the graph doesnt exist there

