Discussion
The figure shows the plot of a function over the interval [-4, 4]. Which one of the options given CORRECTLY identifies the function?
Answer: B
The function is \(|2 - |x||\).
Read the plotted points: \(y = 2\) at \(x = 0\), \(y = 0\) at \(x = \pm 2\), and the lines climb back to \(y = 2\) at \(x = \pm 4\), giving a W shape symmetric about the y-axis. Check \(|2 - |x||\):
- \(x = 0\): \(|2 - 0| = 2\)
- \(x = \pm 2\): \(|2 - 2| = 0\)
- \(x = \pm 4\): \(|2 - 4| = 2\)
\(|2 - x|\) is a single V with its vertex at \(x = 2\) and is not symmetric (it equals 6 at \(x = -4\)). \(|2 + |x||\) is never below 2, so it cannot touch zero. \(2 - |x|\) has the right peak but goes negative beyond \(x = \pm 2\), reaching \(-2\) at \(x = \pm 4\), while the plot never drops below the axis.
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