For positive real numbers S and K, the function H_K(S) is defined as: H_K(S) = (S - K, 0). The max function is defined as: (a, b) = cases a, & when a > b \\ b, & when a ≤ b cases The graph below shows the plot of a function N(S) versus S. N(S) can be expressed as _____.

GATE CSE 2026 Session 1 Q8: Express a ramp function using max(S − K, 0) terms

For positive real numbers $S$ and $K$ , the function $H_K(S)$ is defined as: $H_K(S) = \max(S - K, 0)$ . The max function is defined as:

$\max(a, b) = \begin{cases} a, & \text{when } a > b \\ b, & \text{when } a \le b \end{cases}$

The graph below shows the plot of a function $N(S)$ versus $S$ .

$N(S)$ can be expressed as _____.

Try it: multiple choice: exactly one correct option

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Answer: A (official GATE 2026 final answer key)

Concept used: Piecewise-linear functions as sums of shifted ramps: each kink adds or removes a slope of 1.

First step: The slope turns on at $S = 10$ and turns off at $S = 20$ ; write a ramp starting at 10 minus a ramp starting at 20.

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key