Graph g(x)=x^3-2

Problem

g(x)=x3−2

Solution

1. Identify the parent function as ƒ(x)=x3 which is a cubic function with a characteristic "S" shape passing through the origin (0,0)

2. Determine the transformation by observing the constant −2 subtracted from the parent function.

3. Apply a vertical shift downward by 2 units to all points on the parent graph.

4. Calculate key points to plot the graph:

   • When x=−1 g*(−1)=(−1)3−2=−3

   • When x=0 g(0)=(0)3−2=−2 (the y-intercept).

   • When x=1 g(1)=(1)3−2=−1

   • When x=2 g(2)=(2)3−2=6

5. Sketch the curve through the points (−1,−3) (0,−2) (1,−1) and (2,6) ensuring the inflection point is at (0,−2)

Final Answer

g(x)=x3−2

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