Which functions are symmetric with respect to the y-axis? check all that apply.
a. f(x) = |x|
b. f(x) = |x| + 3
c. f(x) = |x + 3|
d. f(x) = |x| + 6
e. f(x) = |x – 6|
f. f(x) = |x + 3| – 6

Answer : A, B  and D

We need to find the functions that are symmetric with respect to the y-axis

A. f(x) = |x| is always symmetric about y axis because vertex is at origin and we will get V - shaped graph.

B. f(x) = |x| + 3 is symmetric about y axis. We know f(x) = |x| is always symmetric about y axis. 3 is added at the end so the graph will be shifted up. So the graph is still symmetric about y axis.

C. f(x) = |x + 3| is not symmetric about y axis because 3 is added with x  so  we move the graph of f(x)= |x|  three units to the left.

D. f(x) = |x| + 6 is symmetric about y axis.   f(x) = |x| is always symmetric about y axis. 6 is added at the end so the graph will be shifted up. So the graph is still symmetric about y axis.

E. f(x) = |x – 6|  is not symmetric about y axis because 6 is subtracted with x  so  we move the graph of f(x)= |x|  six units to the right.

F. f(x) = |x + 3| – 6 is not is symmetric about y axis.  3 is added with x and 6 is subtracted at the end. so we move the graph f(x) = |x| 6 units down and 3 units left. So the graph is not symmetric about y axis.