Where is the function continuous? Differentiable? Use the grap...

Question

Where is the function continuous? Differentiable? Use the graph of f in the figure to do the following.

a. Find the values of x in (0, 3) at which f is not continuous.

Accepted Answer

Welcome back, everyone. Analyze the graph of the function j of X to find the x value in the interval from 0 to 6, not inclusive, at which J is not continuous. We're given for answer choices A says x equals 5, B X equals 2, C X equals 3, and D X equals 6. So whenever we solve a continuity problem graphically, we have to recall that a fun. is simply continuous if we can draw it without raising our hand. So if we start at the beginning of the interval at 0, and if we follow the red curve, we can definitely draw that smooth curve from 0 to 2. But then from 2 to 4, well, essentially we have to raise our hand to move to a different y value, and then we're going down, then we're going up from From 2 to 6, well, essentially we can draw that part of the function without raising our hand from the graph, right? So this means that those two parts are actually continuous. However, at 0.2 this is where we had to raise our hand, right, to draw the second part of the curve, meaning we have a discontinuity point, and here we have a break. Within the graph, which is a discontinuity and we can prove that because if we recall one of the conditions for continuity, the limit. From one side of the point should be equal to the value of the function at that point. Notice that the limit. Of the function as we approach 2 from the left is 6, but the value of the function at 0.2 is defined at a filled or solid point, and that's 7, and they're not equal to each other, indicating that we have that break. So essentially we can say that this function is not continuous. At X equals 2 because this is where we have a break. So our final answer to this problem corresponds to the answer choice B. Thank you for watching.

Where is the function continuous? Differentiable? Use the graph of f in the figure to do the following. <IMAGE>
a. Find the values of x in (0, 3) at which f is not continuous.

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Where is the function continuous? Differentiable? Use the graph of f in the figure to do the following. <IMAGE>a. Find the values of x in (0, 3) at which f is not continuous.

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Where is the function continuous? Differentiable? Use the graph of f in the figure to do the following. <IMAGE>
a. Find the values of x in (0, 3) at which f is not continuous.