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)
Responses

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 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.
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.

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 range is P≤0
, so the additional pay for an employee only has negative values.

Answer 1

To analyze the function \( P = 0.15|d| + 25 \), let's break down its key features:

1. **Vertex**:
The vertex of the function is at \( (0, 25) \). This means that when the distance \( d \) is 0 miles (i.e., the employee does not travel), the additional pay is $25. This is the minimum amount paid to the employee based on the function.

2. **Behavior of the Function**:
The function is not decreasing; rather, it increases as the absolute value of \( d \) increases due to the coefficient \( 0.15 \) attached to \( |d| \). More specifically, as \( d \) increases (whether in the positive or negative direction), the additional pay \( P \) also increases.

3. **Domain**:
The domain of the function is all real numbers (\( -\infty < d < \infty \)). This means that the employee can travel any distance, whether negative (indicating traveling away from the work site) or positive (indicating traveling towards the work site).

4. **Range**:
The range of the function is \( P \geq 25 \). Since the minimum value of \( P \) occurs at \( d = 0 \) and equals 25, the additional pay can only be $25 or more, never negative.

Given these features, 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.**

The other statements are incorrect based on the function's characteristics:

- It's not a decreasing function; it actually increases.
- The domain is not limited to \( d \leq 0 \); it includes all real numbers.
- The range is \( P \geq 25 \), not \( P \leq 0 \).

So, the correct key feature to highlight is the vertex and its significance regarding the additional pay.