Graph y=1/2x^3

Problem

y=1/2*x3

Solution

1. Identify the parent function as y=x3 which is an odd function that passes through the origin (0,0) and has rotational symmetry about the origin.

2. Determine the transformation, which is a vertical compression by a factor of 1/2 because the coefficient of x3 is between 0 and 1

3. Calculate key points to plot the curve:

• If x=−2 y=1/2*(−2)3=−4

• If x=−1 y=1/2*(−1)3=−0.5

• If x=0 y=1/2*(0)3=0

• If x=1 y=1/2*(1)3=0.5

• If x=2 y=1/2*(2)3=4

4. Plot these points (−2,−4) (−1,−0.5) (0,0) (1,0.5) and (2,4) on a coordinate plane.

5. Sketch a smooth curve through the points, ensuring the graph is flatter near the origin than the standard y=x3 graph.

Final Answer

y=1/2*x3

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