Graph y=3/2x^3

Problem

y=3/2*x^3

Solution

1. Identify the function type as a cubic function of the form y=a*x^3 where a=3/2

2. Determine the symmetry of the function. Since ƒ*(−x)=3/2*(−x)^3=−3/2*x^3=−ƒ(x) the graph is symmetric with respect to the origin (an odd function).

3. Find the intercept. When x=0 y=0 so the graph passes through the origin (0,0)

4. Calculate key points to determine the shape.
   For x=1 y=3/2*(1)^3=1.5
   For x=2 y=3/2*(2)^3=12
   For x=−1 y=3/2*(−1)^3=−1.5
   For x=−2 y=3/2*(−2)^3=−12

5. Analyze the end behavior. As x→∞ y→∞ and as x→−∞ y→−∞

6. Plot the points (0,0) (1,1.5) and (−1,−1.5) and draw a smooth curve that is steeper than a standard y=x^3 graph due to the vertical stretch factor of 1.5

Final Answer

y=3/2*x^3

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