Answer:
We will choose option 3.
Step-by-step explanation:
The piecewise function f(x) has the following definition :
f(x) = 2x - 1, when x < 0 ........... (1)
f(x) = 0, when x = 0 and ........... (2)
f(x) = - 2x + 1, when x > 0 ........... (3)
Now, on a coordinate plane, this piecewise function has 2 lines. The first line goes up from (-2,-5) to a closed circle at (0,-1). The second line has a closed circle at (0, 1) and goes down through (2,-3).
This is because, the point (-2,-5) satisfies equation (1) and as x tends to -0 from equation (1), f(x) tends to -1.
Again the point (2,-3) satisfies equation (3) and as x tends to +0 from equation (3), f(x) tends to 1.
Hence, we will choose option 3. (Answer)