GATE 2016 EE – Question 10

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

Choose the correct expression for $f(x)$ given in the graph.

[Graph: a straight line rises from $(-3, -2)$ to a peak at $(1, 2)$, then falls in a straight line to $(3, 0)$.]

Diagram for GATE 2016 EE question 10

$f(x) = 1 - |x - 1|$
$f(x) = 1 + |x - 1|$
$f(x) = 2 - |x - 1|$
$f(x) = 2 + |x - 1|$

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Show answer and explanation

Correct answer: (C) $f(x) = 2 - |x - 1|$

Explanation

The graph has its peak at $x = 1$ with value 2, so it has the form $2 - |x - 1|$. Check with other points: $f(3) = 2 - 2 = 0$ and $f(-3) = 2 - 4 = -2$, which both match the graph.