Suppose that R(x) = 2 for x < 3 and R(x) = -4 for x >3.
a. What is R(3) if R is left-continuous at x = 3?
b. What is R(3) if R is right-continuous at x = 3?
a. What is R(3) if R is left-continuous at x = 3?
b. What is R(3) if R is right-continuous at x = 3?
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a) if the function is left-continuous at x=3, that means it is continuous from the section where R(x) = 2.
so R(3) would equal 2
b) R(3) = -4 (same reasoning)
If it helps, picture the graph (or draw it out). There would be a discontinuity at x = 3; one side of the function would lead to a hollow dot, and the other would lead to a solid dot. (solid meaning continuous to the dot, hollow meaning discontinuous at the point)
Hope that helps.
so R(3) would equal 2
b) R(3) = -4 (same reasoning)
If it helps, picture the graph (or draw it out). There would be a discontinuity at x = 3; one side of the function would lead to a hollow dot, and the other would lead to a solid dot. (solid meaning continuous to the dot, hollow meaning discontinuous at the point)
Hope that helps.