For positive real numbers S and K, the function HK(S) is defined as: HK(S) =…
2026
For positive real numbers S and K, the function HK(S) is defined as:
HK(S) = max(S - K, 0). The max function is defined as:
The graph below shows the plot of a function N(S) versus S.
N(S) can be expressed as _____.
- A.
𝐻10(𝑆)−𝐻20(𝑆)
- B.
𝐻10(𝑆)−2𝐻20(𝑆)
- C.
-𝐻10(𝑆)+𝐻20(𝑆)
- D.
𝐻15(𝑆)−𝐻20(𝑆)
Attempted by 1 students.
Show answer & explanation
Correct answer: A
H_K(S) = max(S - K, 0) is zero for S <= K and equals S - K for S > K.
For H_10(S) - H_20(S):
- If S <= 10, both terms are zero, so the value is 0.
- If 10 < S <= 20, H_10(S) = S - 10 and H_20(S) = 0, so the value is S - 10.
- If S > 20, H_10(S) = S - 10 and H_20(S) = S - 20, so the value is 10.
This gives exactly the plotted capped ramp: 0 until S = 10, increasing linearly to 10 at S = 20, and then remaining constant at 10. Therefore N(S) = H_10(S) - H_20(S).