Determine whether y is a function of x.
Understand the Problem
The question is asking to evaluate if the variable y can be expressed as a function of the variable x, which implies checking if for every x-value there is exactly one corresponding y-value.
Answer
It depends on the specific situation.
Answer for screen readers
The answer depends on the specific equation or data provided.
Steps to Solve
- Check the definition of a function
A function from x to y must assign exactly one y-value to each x-value. If you can find even a single x-value that corresponds to more than one y-value, then y is not a function of x.
- Use the vertical line test for graphs
If you have a graph, you can use the vertical line test. Draw vertical lines through the graph. If any vertical line intersects the graph at more than one point, then y is not a function of x.
- Analyze the equation or data
If you are given an equation or a set of data points, check to see if each x-value yields exactly one y-value. For example, if the equation is $y = x^2$, each x-value yields exactly one y-value.
The answer depends on the specific equation or data provided.
More Information
Checking whether y is a function of x is fundamental for understanding functional relationships in mathematics. If each x-value has exactly one y-value, y is a function of x.
Tips
A common mistake is assuming y is a function of x without checking for all x-values. Always verify every x-value to ensure there is only one corresponding y-value.
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