When graphing a step function, several key aspects should be considered to accurately represent the function. Here is a detailed, step-by-step breakdown:
1. The intervals where the function is defined:
- A step function is typically defined on specific intervals. This means you need to identify and clearly define the range of values on the x-axis where the function takes particular constant values. This helps in outlining where each 'step' occurs on the graph.
2. Where the function jumps:
- A unique characteristic of a step function is the discontinuities or 'jumps' between the intervals. These are the points where the function value changes abruptly from one constant value to another. It's essential to accurately show these jumps to reflect the true nature of the function.
3. The smoothness of the curve:
- This aspect is not relevant to a step function. Unlike continuous functions, step functions are characterized by their lack of smooth continuity. They have discrete jumps, so considering the smoothness of the curve is not necessary.
4. The endpoints of the intervals:
- The endpoints of the intervals indicate the boundaries where the function's value changes. It's important to identify these points on the x-axis to understand where each step starts and ends. These points are often marked with open or closed circles to denote whether the function includes the endpoint or not.
Therefore, the aspects you should consider when graphing a step function are:
- The intervals where the function is defined
- Where the function jumps
- The endpoints of the intervals
The selected aspects are 1, 2, and 4.
