By using the graph, the limit of the function does not exist (DNE).
What is a limit?
In Mathematics and Euclidean Geometry, a limit is a numerical value which a function approaches (output value) as the input value approaches other values.
Generally speaking, the limit of a function at a given input value does not exist (DNE) when the left-hand limit is not equal to the right-hand limit;
[tex]\lim_{x \to a^-} f(x)\neq \lim_{x \to a^+} f(x)[/tex]
By critically observing the graph of the function shown above, we can logically deduce that the following limits exist or does not exist (DNE);
[tex]\lim_{x \to 2^-} f(x)=5[/tex], when x is less than 2, but infinitesimally close to 2, the output values approach f(x) = 5.
[tex]\lim_{x \to 2^+} f(x)=-3[/tex], when x is greater than 2, but infinitesimally close to 2, the output values get to f(x) = -3.
[tex]\lim_{x \to 2} f(x)=DNE[/tex] because the left-hand limit and right-hand limit are not equal.
Since there is a discontinuity at x = 2, the output value for the function at f(2) does not exist (DNE);
5 ≠ -3
Read more on limit here: brainly.com/question/23343679
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