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

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

Step-by-step 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.

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation:

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3