Problem

Use transformations of the standard cubic function, $f(x)=x^{3}$, to graph the function $h(x)=-(x-6)^{3}$.

Answer

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Answer

The graph of \(h(x)=-(x-6)^{3}\) is the result of these transformations.

Steps

Step 1 :The standard cubic function is \(f(x)=x^{3}\).

Step 2 :The function \(h(x)=-(x-6)^{3}\) is a transformation of the standard cubic function.

Step 3 :The transformation involves a horizontal shift to the right by 6 units and a reflection in the x-axis.

Step 4 :To graph \(h(x)=-(x-6)^{3}\), start by graphing the standard cubic function \(f(x)=x^{3}\).

Step 5 :Then shift the graph 6 units to the right. This corresponds to replacing \(x\) with \(x-6\) in the function.

Step 6 :Finally, reflect the graph in the x-axis. This corresponds to multiplying the function by -1.

Step 7 :The graph of \(h(x)=-(x-6)^{3}\) is the result of these transformations.

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