examday

/TMUA

There are two real numbers $a$ and $b$ with $a>0$, $b>0$. Consider the following statements about the function $f(x)$. Which statement(s) is/are true?

• I. “$f(x-a)$ is symmetric about the point $(a,0)$” is sufficient and necessary for “$f(x)$ is an odd function”.
• II. “$f(x-a)$ is symmetric about the line $x=a$” is sufficient and necessary for “$f(x)$ is an even function”.
• III. “$a=b$” is sufficient and necessary for “$f(x-a)$ and $f(b-x)$ are symmetric about the $y$-axis”.