To determine the value of f(1) for a step function, we first need to understand the characteristics of a step function. A step function is a piecewise constant function that jumps from one value to another without taking on any values in between. It is often represented visually as a series of horizontal lines that change values at specified points along the x-axis.
For instance, let’s consider a simple step function defined as follows:
f(x) = {
0, if x < 0
1, if 0 ≤ x < 2
2, if 2 ≤ x < 4
3, if x ≥ 4
}
In this example, the function has different values for specified ranges of x. To find f(1), we look at the definition of the function:
- For x < 0, f(x) = 0.
- For 0 ≤ x < 2, f(x) = 1.
- For 2 ≤ x < 4, f(x) = 2.
- For x ≥ 4, f(x) = 3.
Since 1 falls within the range of 0 ≤ x < 2, we find that:
f(1) = 1
Therefore, the value of f(1) when the step function is graphed is 1.