How can we determine if f(1) for the function f(x) = 8 – 2x^2 is a function?

To determine whether f(1) is a function for the given expression f(x) = 8 – 2x2, we first need to evaluate f(1).

1. **Substituting x with 1**: We start by replacing x in the function with 1:

f(1) = 8 – 2(1)2

2. **Calculating**: Now, we perform the calculations step by step:

  • (1)2 = 1
  • 2(1) = 2
  • 8 – 2 = 6

So, we find that f(1) = 6.

3. **Understanding Function Behavior**: The output f(1) = 6 is a single value derived from an input. A function is defined as a relation where each input is associated with exactly one output. Since 1 is a specific input leading to the specific output 6, we can confirm that f(1) is indeed a function.

4. **Conclusion**: Therefore, we can conclude that f(1) not only yields a result but also adheres to the definition of a function. Every input we use in the function f(x) = 8 – 2x2 provides a consistent output, assuring that f(1) remains a function.

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