Question

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 1

Hello,

y=|x|+a is symmetric
==> Answer A,B,D

Answer 2

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.