The graph of y=x^(1/3) and y= -2x^(1/2) is a curve that intersects at the origin (0,0) and extends outwards in both positive and negative directions. The curve for y=x^(1/3) is steeper and approaches the x-axis more quickly than the curve for y= -2x^(1/2), which is flatter and approaches the x-axis more gradually.
The key features of the graph of y=x^(1/3) and y= -2x^(1/2) are the origin (0,0), the curves that intersect at the origin, and the direction and steepness of the curves as they extend outwards.
The domain of the graph of y=x^(1/3) and y= -2x^(1/2) is all real numbers. The range for y=x^(1/3) is all real numbers, while the range for y= -2x^(1/2) is only positive real numbers.
The x-intercepts of the graph of y=x^(1/3) and y= -2x^(1/2) are at the origin (0,0). The y-intercept of y=x^(1/3) is also at the origin, while the y-intercept of y= -2x^(1/2) is not defined.
The direction of the curves for y=x^(1/3) and y= -2x^(1/2) can be determined by looking at the coefficients of the exponents. The coefficient for y=x^(1/3) is 1, which means the curve will point upwards as x increases. The coefficient for y= -2x^(1/2) is -2, which means the curve will point downwards as x increases.