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GATE 2018 ME (ME1) – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Which function describes the plotted graph?

Diagram for GATE 2018 ME (ME1) question 9
  1. $y=\bigl||x|+1\bigr|-2$
  2. $y=\bigl||x|-1\bigr|-1$
  3. $y=\bigl||x|+1\bigr|-1$
  4. $y=\bigl||x-1|-1\bigr|$

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Show answer and explanation

Correct answer: (B) $y=\bigl||x|-1\bigr|-1$

Explanation

The graph is symmetric about the y-axis, with zeros at x = 0, ±2 and minima −1 at x = ±1. The function $y=\bigl||x|-1\bigr|-1$ has precisely these features (B).