Question

What is the range of signum function which is a piecewise function f(x) = sgnx 

Answer 1

The range of the signum function, denoted by f(x) = sgn(x), is typically defined as the set {-1, 0, 1}. 

The signum function returns -1 for negative values of x, 1 for positive values of x, and 0 for x = 0. Therefore, the range is those three possible values.

Answer 2

The signum function, often denoted as sgn(x), is a piecewise function that returns:

1. sgn(x) = 1 when x > 0 (positive numbers)

2. sgn(x) = 0 when x = 0 (zero)

3. sgn(x) = -1 when x < 0 (negative numbers)

So, the range of the signum function is the set {-1, 0, 1}. It only takes on these three values depending on whether the input is negative, zero, or positive.

Answer 3

The range of the signum function, denoted as sgn(x), is [-1, 1]. It takes the value -1 for x < 0, 1 for x > 0, and 0 when x = 0.

Answer 4

The signum function, denoted as \( \text{sgn}(x) \), is a piecewise function defined as follows:

\[ \text{sgn}(x) = \begin{cases} -1 & \text{if } x < 0 \\ 0 & \text{if } x = 0 \\ 1 & \text{if } x > 0 \end{cases} \]

The range of the signum function is the set of possible output values it can take. In this case, the range is \(\{-1, 0, 1\}\) because these are the only values that the function can output based on its definition for negative, zero, and positive values of \(x\), respectively.