Question
Make a graph on a sheet of paper. Then answer the question.The function P=0.15|d|+25 can be used to find the amount of additional pay an employee receives each day for traveling d miles to a work site.What do the key features of the function reveal?(1 point)ResponsesThe range is P≤0, so the additional pay for an employee only has negative values.The range is cap p is less than or equal to 0 , so the additional pay for an employee only has negative values.There is a vertex at (0,25) which indicates that when an employee travels 0 miles to the work site, the amount of additional pay is $25.There is a vertex at open paren 0 comma 25 close paren which indicates that when an employee travels 0 miles to the work site, the amount of additional pay is $25.The domain is d≤0, so the distances from the work site are only negative values.The domain is d is less than or equal to 0 , so the distances from the work site are only negative values.The function is a decreasing function, so as the distance an employee travels to a work site increases, the amount of additional pay decreases at a constant rate.
Answers
GPT-4o mini
To analyze the function \( P = 0.15|d| + 25 \), let's break down its key features:
1. **Vertex**: The vertex of this function occurs at \( d = 0 \). At this point, the additional pay \( P \) is \( P = 0.15|0| + 25 = 25 \). This means that when an employee travels 0 miles to the work site, they receive an additional pay of $25.
2. **Slope and Behavior**: The function has a positive slope of \( 0.15 \) for both positive and negative values of \( d \). This indicates that as the absolute value of the distance \( |d| \) increases, the additional pay \( P \) increases as well, not decreases. The more miles an employee travels, the more additional pay they will receive.
3. **Range**: The range of \( P \) begins at 25 (when \( d = 0 \)) and increases without bound as \( |d| \) increases. Therefore, the range is \( P \geq 25 \).
4. **Domain**: The domain of the function is all real numbers since \( d \) can take any value, both positive and negative.
Now, with these features in mind, let's evaluate the provided response options:
- **The range is \( P \leq 0 \)**: This statement is incorrect. The range starts at $25 and goes upwards.
- **The vertex at \( (0, 25) \)**: This is correct and indicates the additional pay when traveling 0 miles.
- **Domain \( d \leq 0 \)**: This is incorrect; the domain includes all real numbers (positive and negative).
- **Function is decreasing**: This is also incorrect. The function is increasing due to the positive coefficient of \( |d| \).
Thus, the correct response is:
**There is a vertex at \( (0, 25) \) which indicates that when an employee travels 0 miles to the work site, the amount of additional pay is $25.**
1. **Vertex**: The vertex of this function occurs at \( d = 0 \). At this point, the additional pay \( P \) is \( P = 0.15|0| + 25 = 25 \). This means that when an employee travels 0 miles to the work site, they receive an additional pay of $25.
2. **Slope and Behavior**: The function has a positive slope of \( 0.15 \) for both positive and negative values of \( d \). This indicates that as the absolute value of the distance \( |d| \) increases, the additional pay \( P \) increases as well, not decreases. The more miles an employee travels, the more additional pay they will receive.
3. **Range**: The range of \( P \) begins at 25 (when \( d = 0 \)) and increases without bound as \( |d| \) increases. Therefore, the range is \( P \geq 25 \).
4. **Domain**: The domain of the function is all real numbers since \( d \) can take any value, both positive and negative.
Now, with these features in mind, let's evaluate the provided response options:
- **The range is \( P \leq 0 \)**: This statement is incorrect. The range starts at $25 and goes upwards.
- **The vertex at \( (0, 25) \)**: This is correct and indicates the additional pay when traveling 0 miles.
- **Domain \( d \leq 0 \)**: This is incorrect; the domain includes all real numbers (positive and negative).
- **Function is decreasing**: This is also incorrect. The function is increasing due to the positive coefficient of \( |d| \).
Thus, the correct response is:
**There is a vertex at \( (0, 25) \) which indicates that when an employee travels 0 miles to the work site, the amount of additional pay is $25.**