Answer :
To determine which situation can be graphed using a step function, we need to understand what a step function is. A step function is a piecewise constant function, meaning its value jumps abruptly from one constant value to another.
Let’s analyze each of the given options in detail:
1. Each output is the place value of the ones digit for an input.
- This would mean that for any input number, the output is the digit in the ones place (0-9). It doesn’t have abrupt jumps from one constant value to another but changes according to the digit in the ones place.
2. Each output is the remainder when an input is divided by 5.
- This means when you divide any integer by 5, the remainder will be one of 0, 1, 2, 3, or 4. For example:
- 10 divided by 5 gives a remainder of 0.
- 11 divided by 5 gives a remainder of 1.
- 12 divided by 5 gives a remainder of 2.
- This pattern repeats periodically every 5 integers, creating abrupt jumps at each interval (5, 10, 15, etc.). Hence, it features the characteristic of a step function with these discrete output values.
3. Each output is the result of determining the absolute value of the input.
- The absolute value function assigns the non-negative value for any given input. For example, the absolute value of -3 is 3, and the absolute value of 3 is 3. This function does not have abrupt jumps, but rather a consistent change in value based on the input.
4. Each output is the result of rounding an input to the nearest ten.
- When rounding to the nearest ten, the output value changes at specific points (e.g., 14 rounds to 10, but 15 rounds to 20). This function changes values abruptly at points like 14.5 or 15.5, which seems like a step function. But the output values depend on specific intervals and conditions, making it different from a standard step function.
Given the analysis, we conclude that the correct situation that can be graphed using a step function is:
Each output is the remainder when an input is divided by 5.
Let’s analyze each of the given options in detail:
1. Each output is the place value of the ones digit for an input.
- This would mean that for any input number, the output is the digit in the ones place (0-9). It doesn’t have abrupt jumps from one constant value to another but changes according to the digit in the ones place.
2. Each output is the remainder when an input is divided by 5.
- This means when you divide any integer by 5, the remainder will be one of 0, 1, 2, 3, or 4. For example:
- 10 divided by 5 gives a remainder of 0.
- 11 divided by 5 gives a remainder of 1.
- 12 divided by 5 gives a remainder of 2.
- This pattern repeats periodically every 5 integers, creating abrupt jumps at each interval (5, 10, 15, etc.). Hence, it features the characteristic of a step function with these discrete output values.
3. Each output is the result of determining the absolute value of the input.
- The absolute value function assigns the non-negative value for any given input. For example, the absolute value of -3 is 3, and the absolute value of 3 is 3. This function does not have abrupt jumps, but rather a consistent change in value based on the input.
4. Each output is the result of rounding an input to the nearest ten.
- When rounding to the nearest ten, the output value changes at specific points (e.g., 14 rounds to 10, but 15 rounds to 20). This function changes values abruptly at points like 14.5 or 15.5, which seems like a step function. But the output values depend on specific intervals and conditions, making it different from a standard step function.
Given the analysis, we conclude that the correct situation that can be graphed using a step function is:
Each output is the remainder when an input is divided by 5.
