Question

You may use a graphing calculator if necessary.

Let the piece-wise function f(x) = x+3, if x<0, or x-3, if x is greater than or equal to 0.

The limit f(x) as x approaches to 1 =

(A) -2

(B) -1

(C) 0

(D) 1

(E) does not exist

Answer 1

The limit of the piece-wise function f(x) as x approaches 1 is -2, which corresponds to option (A), because for x values greater than or equal to 0, the function f(x) = x - 3 is used.

Step-by-step explanation:

The question asks for the limit of the piece-wise function f(x) as x approaches 1. The function is given by f(x) = x + 3 when x < 0, and f(x) = x - 3 when x ≥ 0. Since we are looking for the limit as x approaches 1, we only need to consider the second part of the function for x ≥ 0. Therefore, we substitute 1 into the function to get f(1) = 1 - 3 = -2. Thus, the limit of f(x) as x approaches to 1 is -2, which corresponds to option (A).