Can someone please explain this to me? I’m really confused on how to find the limit with the piecewise function.

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Step-by-step explanation:

You only need to evaluate at the limit point.

f(x) = 4 - x  ; x ≠ 2

Consider the solution if x = 2 (because the limit is x → 2)

                                          f(2) = 4 - (2)

                                                =   2

We know that f(x) = 0  ; x = 2

                                         f(2) = 0

but we are looking for the y- value it approaches - not the y-value it is.

Look at the graph.  You will see that as x gets closer and closer to 2, the y-value gets closer and closer to 2.  This is the limit.

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step-by-step explanation: