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GATE 2018 CE (CE1) – Question 8

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

Which functions describe the graph on their indicated ranges? (i) $y=2x+4$, $-3\le x\le-1$. (ii) $y=|x-1|$, $-1\le x\le2$. (iii) $y=\bigl||x|-1\bigr|$, $-1\le x\le2$. (iv) $y=1$, $2\le x\le3$.

Diagram for GATE 2018 CE (CE1) question 8
  1. i, ii and iii only
  2. i, ii and iv only
  3. i and iv only
  4. ii and iv only

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Show answer and explanation

Correct answer: (B) i, ii and iv only

Explanation

The left segment joins (−3,−2) to (−1,2), so its equation is $y=2x+4$: i holds. The central V is $|x-1|$: ii holds. Expression iii gives 0 at x = −1 instead of the plotted 2, so it fails. The final segment has y = 1: iv holds. Answer B.