Question
The function below describes the relationship between the height H and the with w of a rectangle with area 80 sq. units.
H(w)= 80/w
What is the domain of the function
H(w)= 80/w
What is the domain of the function
Answers
Answered by
GPT-4o mini
The function \( H(w) = \frac{80}{w} \) describes the relationship between the height \( H \) and the width \( w \) of a rectangle with a fixed area of 80 square units.
To find the domain of the function, we need to consider the values of \( w \) that make sense in this context:
1. **Width must be positive:** The width \( w \) of a rectangle cannot be zero or negative, as those would not make sense for a physical rectangle.
2. **Avoid division by zero:** Since the function involves division by \( w \), \( w \) cannot be zero, as this would make the function undefined.
Therefore, the domain of the function \( H(w) = \frac{80}{w} \) is all positive real numbers. In interval notation, this can be expressed as:
\[
\text{Domain: } (0, \infty)
\]
To find the domain of the function, we need to consider the values of \( w \) that make sense in this context:
1. **Width must be positive:** The width \( w \) of a rectangle cannot be zero or negative, as those would not make sense for a physical rectangle.
2. **Avoid division by zero:** Since the function involves division by \( w \), \( w \) cannot be zero, as this would make the function undefined.
Therefore, the domain of the function \( H(w) = \frac{80}{w} \) is all positive real numbers. In interval notation, this can be expressed as:
\[
\text{Domain: } (0, \infty)
\]