Problem

Graph the following function using transformation techniques. \[ g(t)=\frac{1}{2} x^{3} \]

Solution

Step 1 :The function is a cubic function, which typically has the shape of an 'S' curve.

Step 2 :The coefficient \(\frac{1}{2}\) in front of the \(x^{3}\) term will affect the steepness of the curve, but not its basic shape.

Step 3 :The graph of the function \(g(t)=\frac{1}{2} x^{3}\) is an 'S' curve that becomes steeper as \(x\) increases or decreases.

Step 4 :\(\boxed{\text{The coefficient } \frac{1}{2} \text{ in front of the } x^{3} \text{ term makes the curve less steep than the graph of } x^{3}.}\)

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Source: https://solvelyapp.com/problems/34168/

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