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GATE 2023 ME – Question 12

Engineering Mathematics · Calculus: Limit, continuity, differentiability, mean value theorems and indeterminate forms · 1 mark · Multiple choice

The figure shows the plot of a function over the interval [-4, 4]. Which one of the options given CORRECTLY identifies the function?

a graph that is zero at $x = -2$ and $x = 2$, rises to a peak of 2 at $x = 0$ (with straight sloping segments), and rises again towards $x = \pm 4$.
  1. $|2 - x|$
  2. $|2 - |x||$
  3. $|2 + |x||$
  4. $2 - |x|$

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Show answer and explanation

Correct answer: (B) $|2 - |x||$

Explanation

The function is symmetric about the y-axis, so it involves $|x|$. It equals 2 at $x = 0$ and is zero at $x = \pm 2$, and then it increases again for $|x| > 2$. For $|2 - |x||$: at $x = 0$ it is 2, at $x = \pm 2$ it is 0, and for $|x| > 2$ it is $|x| - 2$, which rises again. Option D, $2 - |x|$, would become negative beyond 2, and option C is never zero. Option A is not symmetric.