If point $(4,5)$ is on the graph of a function, which equation must be true?
A. $f(5)=4$
B. $f(5,4)=9$
C. $f(4)=5$
D. $f(5,4)=1
Answer (2)
The problem states that the point ( 4 , 5 ) lies on the graph of a function f .
This means that when the input to the function is 4 , the output is 5 , which can be written as f ( 4 ) = 5 .
We examine the given options and determine that f ( 4 ) = 5 is the equation that must be true.
Therefore, the answer is f ( 4 ) = 5 .
Explanation
Understanding the Problem If the point ( 4 , 5 ) is on the graph of a function f , it means that when the input to the function is 4 , the output is 5 . In other words, f ( 4 ) = 5 . We need to check which of the given equations matches this condition.
Analyzing the Options Let's examine each option:
f ( 5 ) = 4 : This means when the input is 5 , the output is 4 . This is not necessarily true based on the given information.
f ( 5 , 4 ) = 9 : This notation is unusual and doesn't fit the standard function notation where a single input produces an output. It's unlikely to be correct.
f ( 4 ) = 5 : This means when the input is 4 , the output is 5 . This matches the given information that the point ( 4 , 5 ) is on the graph of the function.
f ( 5 , 4 ) = 1 : Similar to option 2, this notation is unusual and unlikely to be correct.
Conclusion Based on the analysis, the equation that must be true is f ( 4 ) = 5 .
Examples
Imagine you're tracking the growth of a plant. If after 4 days, the plant has grown to a height of 5 inches, you can represent this as f ( 4 ) = 5 , where f is the function that maps the number of days to the height of the plant. This concept is useful in various real-world scenarios, such as modeling population growth, analyzing financial data, or understanding the relationship between variables in scientific experiments. By understanding functions, you can make predictions and gain insights into how different quantities are related.
The equation that must be true given that the point ( 4 , 5 ) is on the graph of a function is f ( 4 ) = 5 . This reflects the relationship where the input 4 leads to the output 5 . Thus, the correct option is C: f ( 4 ) = 5 .
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