In Exercises 75–78, list the quadrant or quadrants satisfying each condition.x^3 > 0 and y^3 <0

The Cartesian plane is divided into four quadrants based on the signs of the x and y coordinates. Quadrant I has both x and y positive, Quadrant II has x negative and y positive, Quadrant III has both x and y negative, and Quadrant IV has x positive and y negative. Understanding these quadrants is essential for determining where specific conditions hold true.

Inequalities express a relationship where one side is not equal to the other, often involving greater than (>) or less than (<) symbols. In this case, x^3 > 0 indicates that x must be positive, while y^3 < 0 indicates that y must be negative. Solving these inequalities helps identify the values of x and y that satisfy the given conditions.

Cubic functions, such as f(x) = x^3, exhibit specific behaviors based on the sign of x. For positive x, the output is positive, and for negative x, the output is negative. This characteristic is crucial for understanding the conditions x^3 > 0 and y^3 < 0, as it directly influences the signs of x and y in the context of the quadrants.