If x<0, which of the following is negative?

Question

A.) -x

B.) x²

C.) x³

D.) 1/-x

Answer 1

C is negative

x^3<0 if x<0

try a couple specific examples: Let x=-2 <0

then x^3 = (-2)(-2)(-2) = 4(-2) = -8 <0

if x=-2, then x^3 =-8,

or x=-1, then x^3 = (-1)(-1)(-1) = (1)(-1) = -1

if x=-1, x^3=-1

x^3 graphically is in the 1st and 3rd quadrants where x and x^3 are the same sign,

so if one is negative so is the other

A) -x is >0 if x<0 --x=x. try x=-2, then --2=2>0 they're opposite signs

graph y=-x, it's a downward sloping line, which is either in 2nd or 4th quadrants

where x and -x are opposite signs. If x is negative, -x is positive

B) x^2 is always positive. It's an upward opening parabola, which is in quadrants 1 and 2, graphically.

when x<0, x^2 is positive. if x=-2 <0, then x^2 = (-2)(-2) = +4 >0

D) 1/-x is a rectangular hyperbola, entirely in either quadrant 2 or 4, where x and 1/-x are opposite signs, similar to A). If x<0, then 1/-x>0. let x=-2, then 1/-x = 1/--2 = 1/2>0