a(x) 1. Shown at the right are the graphs of three func- tions. Some observation
ID: 1770073 • Letter: A
Question
a(x) 1. Shown at the right are the graphs of three func- tions. Some observations about the graphs: each graph crosses the z-aris at a/2; b(x) is antisym- metric about a/2; and a(z) =-c(x). (a) Estimate whether the following inner prod- b(x) ucts are positive, negative, or zero. In each case, explain your reasoning. i. a(ar) and b() ii. a(a) and c(x) ii. b(x) and c(x) (b) Rank the three inner products above by ab- c(x) solute value from the greatest to the least. Briefly explain how you performed your ranking.Explanation / Answer
1a)
i. The inner product of a(x) and b(x) is positive because a(x) and b(x) have same parity and positive part of a(x) has more area than its negative part.
ii. The inner product of a(x) and c(x) is negative because a(x) and c(x) have opposite parity.
iii. The inner product of c(x) and b(x) is negative because c(x) and b(x) have opposite parity.
Inner product of a(x)c(x) > Inner product of a(x)b(x) = Inner product of c(x)b(x).
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