GATE CS 2016 Set 2 Q.10 (GA Q.10): Quantitative Aptitude

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

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

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

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

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

Official answer and solution

Solution

Identify the vertex and slope of the triangular absolute value curve from the graph to deduce the algebraic expression.

The graph shows a piecewise-linear curve with a single sharp peak (vertex) opening downwards in an inverted V-shape.

Peak / Vertex coordinates: The peak of the graph occurs at $(x, y) = (1, 2)$ .
An inverted absolute value function with vertex at $(h, k)$ has the form:

f(x) = k - a|x - h|

Substituting $h = 1$ and $k = 2$ :

f(x) = 2 - a|x - 1|

Determine the slope $a$ : Look at other identifiable grid intersections on the plot:

At $x = 0$ , the graph passes through $(0, 1)$ : $1 = 2 - a|0 - 1| = 2 - a \implies a = 1$
At $x = 3$ , the graph intersects the x-axis at $(3, 0)$ : $f(3) = 2 - 1|3 - 1| = 2 - 2 = 0$
At $x = -3$ , the graph terminates at $(-3, -2)$ : $f(-3) = 2 - |-3 - 1| = 2 - 4 = -2$

All points match $a = 1$ .

Therefore, the function represented by the graph is:

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

This corresponds to option (C).

Final answer

Common trap

Selecting option (D) $2 + |x - 1|$ , which opens upwards and has a minimum at $(1, 2)$ rather than a maximum.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

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