The function C=320+x

Question

can be used to find the concentration of fertilizer in a mixture that contains a concentration of fertilizer of 15% for 20 ounces of water when x ounces of water are added to the mixture.

What do the key features of the function reveal?

(1 point)
Responses

The function is a decreasing function, so as the number of ounces of water added to the mixture increases, the concentration of fertilizer decreases but not at a constant rate.
The function is a decreasing function, so as the number of ounces of water added to the mixture increases, the concentration of fertilizer decreases but not at a constant rate.

The function is an increasing function, so as the number of ounces of water added to the mixture increases, the concentration of fertilizer increases but not at a constant rate.
The function is an increasing function, so as the number of ounces of water added to the mixture increases, the concentration of fertilizer increases but not at a constant rate.

The domain is x≤0
, so only negative amounts of water are being added to the mixture.
The domain is x is less than or equal to 0 , so only negative amounts of water are being added to the mixture.

There is a horizontal asymptote at C=0
which indicates that when the amount of water added to the mixture increases, the concentration of fertilizer is 0%.
There is a horizontal asymptote at cap c is equal to 0 which indicates that when the amount of water added to the mixture increases, the concentration of fertilizer is 0%.

Answer 1

To analyze the function \( C = 320 + x \) in the context of the concentration of fertilizer in the mixture, let’s break down the features:

1. Form of the Function: The function \( C = 320 + x \) is a linear function. This means that it increases at a constant rate.

2. Interpretation in This Context:

   • In this case, \( x \) represents the number of ounces of water added to the mixture.
   • As \( x \) increases, the total concentration \( C \) also increases.

3. Rate of Increase: The function increases steadily without any indication that the rate of increase changes over time. There are no aspects of the function that indicate a decreasing trend or that it approaches zero asymptotically.

4. Domain: The description does not mention any restrictions on \( x \), meaning it's assumed that \( x \) can take on non-negative values (0 or more ounces added).

5. Asymptotes: There is no horizontal asymptote here because the function continues to increase indefinitely as more water is added.

Based on this analysis, the correct interpretation of the function must acknowledge that it is an increasing function due to the positive coefficient of \( x \), indicating that as the number of ounces of water added to the mixture increases, the concentration of fertilizer increases at a constant rate.

Therefore, the correct response is:

• The function is an increasing function, so as the number of ounces of water added to the mixture increases, the concentration of fertilizer increases but not at a constant rate.

(Note: The last part of the response mentioning "but not at a constant rate" seems incorrect because the rate is constant—it's linear.)