Find the x-value at which f is discontinuous and determine whether f is continuous from the right, from the left, or neither. f(x) = 1 + x^2 if x ≤ 0 4 - x if 0 < x ≤ 4 (x - 4)^2 if x > 4 x = continuous from the right x = continuous from the left x = neither Sketch the graph of f.
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From the given function, we can see that f is defined differently for three different intervals: x ≤ 0, 0 < x ≤ 4, and x > 4. For x ≤ 0, f(x) = 1 + x^2. For 0 < x ≤ 4, f(x) = 4 - x. For x > 4, f(x) = (x - 4)^2. The function is continuous within each of these Show more…
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