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Figure of Function

Source: 1989 National High School Mathematics League, Exam One, Problem 3

February 25, 2020
functionanalytic geometry

Problem Statement

For any function f(x)f(x), in the same rectangular coordinates, figures of function y=f(x−1)y=f(x-1) and y=f(−x+1)y=f(-x+1) (A)\text{(A)} are symmetrical about xx-axis (B)\text{(B)} are symmetrical about line x=1x=1 (C)\text{(C)} are symmetrical about line x=−1x=-1 (D)\text{(D)} are symmetrical about yy-axis
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