Consider the graph of a function g.
Find the point c at which the function has a jump discontinuity but is left-continuous. What value should be assigned to g(c) to make g right-continuous at x = c?
A function g has a jump discontinuity at x = c if and exist, but are not equal.
The graph of g has jump discontinuites at x = 0VV1JcqyBrI= and x = 5.
There is not a jump discontinuity at x = 3 since nhQwv+c4LNyuPzKZSoVQwGwkLo/Hu0z9NCUGxA==.
A function g is left-continuous at x = c if .
Since the problem asks for a point on the graph that is both a jump discontinuity and is left-continuous, check x = 1 and x = 5 to determine if the function is left-continuous at either of these values.
For x = 1: = XvVM00l89Is= and g(1) = XvVM00l89Is=.
For x = 5: = h4XZagboIgc= and g(5) = 0VV1JcqyBrI=.
Thus, g has a jump discontinuity and is left-continuous at x = 0VV1JcqyBrI=.
A function g is right-continuous at x = c if .
Since = 607M7xmPORU=, to redefine the given function g to make it right-continuous at x = 1, assign g(1) = 607M7xmPORU=.