Question

Which functions are symmetric with respect to the y-axis? Check all that apply. f(x) = |x| f(x) = |x| + 3 f(x) = |x + 3| f(x) = |x| + 6 f(x) = |x – 6| f(x) = |x + 3| – 6

Answer 1

$the \: following \: functions \: are \: \\ symmetric \: w.r.t. \: y - axis\\ f(x) = |x| \\ because \: f( - x) = | - x| = |x| = f(x)\\ f(x) = |x| + 3 \\ because \: f( - x) = | - x| + 3 = |x| + 3 = f(x) \\ f(x) = |x| + 6 \\ because \: f( - x) = | - x| + 6 = |x| + 6 = f(x)$