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Chapter 2: Problem 99

Begin by graphing the standard cubic function, \(f(x)=x^{3} .\) Then use transformations of this graph to graph the given function. $$ h(x)=-x^{3} $$

Short Answer

Expert verified
Graph the standard cubic function, then generate the graph of \(h(x)=-x^3\) by reflecting the standard cubic function about the x-axis.

Step by step solution

01

Graphing the Standard Cubic Function

The standard cubic function is \(f(x) = x^3\). It's a curve that increases from left to right. It passes through the origin (0,0) and extends to negative infinity on the left and positive infinity on the right.
02

Reflecting the Curve about the X-axis

The given function \(h(x)=-x^3\) can be obtained from the standard cubic function by reflecting it about the x-axis. This means flipping it upside down. The curve now decreases from left to right. It still passes through the origin (0,0), but extends to positive infinity on the left and negative infinity on the right.

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