Question

Which statement describes the piecewise function when x = –6?

1) f(x) = -6²
2) f(x) = 3x - 18
3) f(x) = -6² + 3(-6) - 18
4) f(x) = -6² + 3(-6)

Answer 1

To determine which statement describes the piecewise function when x = –6, we evaluate each given mathematical expression at that value. Without additional context or the definition of the function over specific intervals, it is not possible to definitively select the correct piecewise function value.

Step-by-step explanation:

When given the value x = –6, we must determine which statement correctly describes the value of the piecewise function at that point. Here are the options evaluated:

1. f(x) = –6² means simply squaring the number –6, which would yield 36.
2. f(x) = 3x - 18 involves substituting –6 for x, which would give us 3(–6) - 18, simplifying to –18 - 18, resulting in –36.
3. f(x) = –6² + 3(–6) - 18 combines the first two statements essentially, which would result in 36 + (–18) - 18, further simplifying to 0.
4. f(x) = –6² + 3(–6) is like the third option, but without subtracting 18, which would give us 36 - 18, resulting in 18.

To accurately identify which statement properly represents the piecewise function's value when x = –6, more information is needed about the function's definition for that specific interval.