Which of the following is not a function?
Understand the Problem
The question is asking to identify which of the given options does not represent a function. This involves analyzing the tables and the equation to determine if any x-values are associated with more than one y-value.
Answer
The first table does not represent a function.
Answer for screen readers
The first table does not represent a function because the x-value of 2 is paired with two different y-values: $y = 4$ and $y = 5$.
Steps to Solve
- Analyze the first table of values
In the first table, let's examine the pairs:
- (1, 3)
- (2, 4)
- (2, 5)
- (3, 9)
Here, the x-value 2 is paired with two different y-values: 4 and 5. This means the first table does not represent a function.
- Check the second table of values
Now, look at the pairs in the second table:
- (-2, 0)
- (0, 1)
- (1, 3)
- (2, 4)
- (3, 7)
Each x-value is associated with only one y-value, which indicates this table does represent a function.
- Examine the equation
The equation given is $y = 3x^2 - 6x + 4$. Since it is a quadratic equation, for each x-value, there is only one corresponding y-value, meaning this does represent a function.
- Review the set of ordered pairs
The set of ordered pairs is:
- (3, 4)
- (6, 5)
- (7, 9)
- (9, 15)
None of the x-values in this list repeat, so this also represents a function.
The first table does not represent a function because the x-value of 2 is paired with two different y-values: $y = 4$ and $y = 5$.
More Information
A function is defined as a relation in which each input (x-value) corresponds to exactly one output (y-value). If an x-value corresponds to multiple y-values, it violates the definition of a function.
Tips
- Ignoring repeating x-values: Always check if any x-values appear more than once with different y-values.
- Confusing equations with functions: Quadratic equations will always yield one y-value for each x-value, so they typically represent functions.
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