Graph of y=x^(1/3) and y= -2x^(1/2)

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To sketch the graphs of y=x^(1/3) and y=-2x^(1/2), start by selecting key x-values such as 0, 1, and -1 to evaluate the corresponding y-values. Understand that y=x^(1/3) has a general shape that is continuous and passes through the origin, while y=-2x^(1/2) is derived from the basic square root function, stretched by a factor of 2 and reflected across the x-axis. This reflection indicates that the graph will only exist for non-negative x-values, producing a downward-opening curve. Combining these insights allows for a more accurate sketch of both functions. Properly visualizing these transformations is essential for effective graphing.
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Homework Statement



What is the procedure or hints of sketching this type of graph (i.e. y=x^(1/3) and y= -2x^(1/2) )? I know how it looks like but i had no ideas what is the proper procedure or technique of sketching them. Please help...

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The Attempt at a Solution



I tried but i really don't know how to do...
 
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choose some x values, for example 0,1, and -1, and then, since you know the general shape of the functions, draw an approximation of the lines.
 
For the second one, presumably you know the shape of y = x^(1/2). Relative to this graph, the graph of -2x^(1/2) is stretched away from the x-axis by a factor of 2 and then reflected across the x-axis.
 

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