Answer: The domain of the function f is [-1,1], meaning that the input values (x) can be any value between -1 and 1, inclusive of -1 and 1.
The function f(-1) = f(0) = f(1) = 0, meaning that the output value (y) is 0 when the input value (x) is -1, 0 or 1.
The limit of f(x) as x approaches -1,0 and 1 is 1. This means that as x gets closer and closer to -1, 0 and 1, the output value (y) approaches 1.
A possible graph of a function with these properties is a function that has a horizontal asymptote at y=1, and intersects the x-axis at -1, 0, and 1. It means that the function approaches y =1 as x gets closer to -1, 0, and 1 but never reach the point. Also, the function is zero at -1, 0, and 1.
This function is called the absolute value function, and it can be represented by f(x) = |x|.
However, the graph you provided in the question is not correct. The function is not a parabola, it's a step function. The graph is not smooth and it has vertical lines at -1, 0, 1.
Explanation: