Make a graph on a sheet of paper. Then answer the question.

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

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.

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 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.

Answer 1

Let's analyze the function \( P = 0.15|d| + 25 \) to understand its key features.

1. Type of Function:

   • This function is not a decreasing function; rather, it is an increasing function because as the absolute distance \( |d| \) increases, the term \( 0.15|d| \) increases, leading to a higher value of \( P \).

2. Vertex:

   • The vertex of this function is indeed at the point \( (0, 25) \). This indicates that when an employee travels 0 miles to the worksite, the additional pay they receive is $25. This is the minimum additional pay since any distance traveled (positive or negative) would only increase the amount of pay.

3. Domain:

   • The domain of this function is all real numbers, \( d \in \mathbb{R} \). It can take both negative and positive values representing distances traveled either towards or away from the worksite.

4. Range:

   • The range of the function \( P \) starts from 25 and goes to infinity, so \( P \geq 25 \). The additional pay will never be negative; it will always be at least $25.

Based on this analysis, the following response accurately reflects the key features of the function:

• "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."

This statement correctly identifies the vertex and its implication regarding the additional pay.

The other options provided are incorrect for the reasons mentioned above.