jennaskim said:Find the points of discontinuity: f(x) = x + 1 , for x < 1 and 1/x for x ≥ 1?
^ supposed to be a piece-wise function.
State whether f is left- or right-continuous at each point of discontinuity.
I'm having difficulty figuring this out... please help?
jennaskim said:Well i tried graphing it...but I STILL DON'T UNDERSTAND
jennaskim said:Well i tried graphing it...but I STILL DON'T UNDERSTAND
A point of discontinuity is a point on a graph where the function is either undefined or has a jump in values. This means that the function is not continuous at that point.
To determine the points of discontinuity for a piecewise function, you need to check the values of the function at the boundary between the two pieces. In this case, we need to check the value of f(1) since the function changes at that point.
No, the function is not continuous at x = 1 since the function has a jump in values at that point.
The function has a jump discontinuity at x = 1 since the value of the function changes abruptly from x + 1 to 1/x at that point.
Yes, a function can have multiple points of discontinuity. In this case, the function has one point of discontinuity at x = 1, but it could have more depending on the function's behavior.