Is y = 11 a function?
Understand the Problem
The question is asking whether the expression 'y = 11' represents a function. A function is defined as a relation where each input has a single output. In this case, for any input value of x, y will always equal 11, indicating that it is indeed a function.
Answer
Yes, the expression $y = 11$ represents a function.
Answer for screen readers
Yes, the expression $y = 11$ represents a function.
Steps to Solve
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Identify the expression The expression given is $y = 11$.
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Determine the input-output relationship For any input value of $x$, the output value of $y$ is constant. This means:
- No matter what value $x$ takes, $y$ will always be $11$.
- Evaluate the definition of a function According to the definition of a function:
- Each input must have exactly one corresponding output.
- In this case, the input $x$ can take any real number, and the output $y$ will consistently be $11$.
- Conclusion Since there is a unique output for each input, it confirms that $y = 11$ represents a function.
Yes, the expression $y = 11$ represents a function.
More Information
The expression $y = 11$ is an example of a constant function, where the output does not change regardless of the input. Such functions are often represented graphically as horizontal lines on a Cartesian plane.
Tips
A common mistake is to assume that the variable $y$ must depend on $x$. In constant functions like $y = 11$, $y$ does not change with $x$, but it still satisfies the criteria of a function.
