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Chapter 1: Problem 92

Determine whether the statement is true or false. Justify your answer. The set of ordered pairs \(\\{(-8,-2),(-6,0),(-4,0)\) \((-2,2),(0,4),(2,-2)\\}\) represents a function.

Short Answer

Expert verified
The statement is true. The set of ordered pairs \((-8,-2),(-6,0),(-4,0),(-2,2),(0,4),(2,-2)\) does represent a function because each x-value corresponds to exactly one y-value.

Step by step solution

01

Understand the Definition of Function

Recall the definition of a function in the context of ordered pairs. In a function, every input (x-value) must correspond to exactly one output (y-value). This means there cannot be repeat x-values with different y-values.
02

Examine the Ordered Pairs

Now let's examine the set of ordered pairs \((-8,-2),(-6,0),(-4,0),(-2,2),(0,4),(2,-2)\). Look at the x-values of each pair. We should ensure that no x-value appears more than once with a different corresponding y-value.
03

Drawing Conclusion

In looking through the list, we can see that each x-value corresponds to exactly one y-value. There are no instances where an x-value corresponds to more than one y-value. Therefore, this set of ordered pairs does represent a function.

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