Question
Question 14 of 20 Which of the following shows the situation below in function notation? The depth of a lake at a certain point, which is a function of the distance of that point from shore, is 30 feet.
Ask by Norris Santiago. in the United States
Jan 24,2025
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Answer
\[ f(x) = 30 \]
Solution
To represent the situation in function notation:
- **Let \( x \)** represent the distance of a point from the shore.
- **Let \( f(x) \)** represent the depth of the lake at that point.
Given that the depth is always 30 feet regardless of the distance from the shore, the function can be written as:
\[ f(x) = 30 \]
This indicates that for any value of \( x \) (distance from the shore), the depth \( f(x) \) remains constant at 30 feet.
**Answer:**
\[ f(x) = 30 \]
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Simplify this solution Mind Expander
In function notation, we can express the depth \( D \) of the lake at a certain distance \( d \) from the shore as \( D(d) = 30 \). This means that regardless of how far you are from the shore (the distance \( d \)), the depth remains consistently 30 feet. Function notation serves as a neat shorthand for illustrating relationships between variables. In this case, it signifies that there's no change in depth as you move away from the shore, making it easy to recognize the lake's characteristics in mathematical terms. So, next time you're at the lake, feel free to impress your friends with that fun fact!
