TMUA Official 2018 Paper 2 · Question 10

The function $f(x)$ is defined for all real numbers.

Consider the following three conditions, where $a$ is a real constant:

Which of these conditions is/are necessary and sufficient for the graph of $y=f(x)$ to have reflection symmetry in the line $x=a$ ?

	Condition I is necessary and sufficient	Condition II is necessary and sufficient	Condition III is necessary and sufficient
A	yes	yes	yes
B	yes	yes	no
C	yes	no	yes
D	yes	no	no
E	no	yes	yes
F	no	yes	no
G	no	no	yes
H	no	no	no

ABCDEFGH

examday

	Condition I is necessary and sufficient	Condition II is necessary and sufficient	Condition III is necessary and sufficient
A	yes	yes	yes
B	yes	yes	no
C	yes	no	yes
D	yes	no	no
E	no	yes	yes
F	no	yes	no
G	no	no	yes
H	no	no	no

	Condition I is necessary and sufficient	Condition II is necessary and sufficient	Condition III is necessary and sufficient
A	yes	yes	yes
B	yes	yes	no
C	yes	no	yes
D	yes	no	no
E	no	yes	yes
F	no	yes	no
G	no	no	yes
H	no	no	no

	Condition I is necessary and sufficient	Condition II is necessary and sufficient	Condition III is necessary and sufficient
A	yes	yes	yes
B	yes	yes	no
C	yes	no	yes
D	yes	no	no
E	no	yes	yes
F	no	yes	no
G	no	no	yes
H	no	no	no