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

Answer

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Answer

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

Steps

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

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

Answer

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