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 + 31
f(x) = [x] + 6
f(x) = |x - 61
f(x) = 5x + 31 - 6

Answer 1

f(x) = |x|, f(x) = [x] + 6

Explanation:

Almost all of these are absolute values equations, which means the y doesn't change if x is positive or negative. The first one is the parent form, which is the simplest equation of the absolute equation, so it's symmetric with respect to the y-axis. The second equation is translated 3 units to the left, and the third is translated 31 to the left. The forth is translated 6 up, so it's still symmetric with respect to the y-axis. The fifth is translated 61 units left, and the last one is simply a line, which isn't symmetric.