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Chapter 1: 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
The graph of \(h(x)=-x^3\) is the reflection of the graph of \(f(x)=x^3\) over the x-axis, resulting in an inverted curvy 'S' shape in the second and fourth quadrants.

Step by step solution

01

Graph the standard cubic function

Start by graphing the standard cubic function \(f(x)=x^3\). This function looks like a curvy 'S' in the first and third quadrants. The highest and lowest points in the graph don't have any bounds.
02

Understand the given transformation

The aim is to graph the function \(h(x) = -x^3\). The negative sign in front of \(x^3\) is a reflection over the x-axis according to function transformations
03

Apply transformations to graph the given function

Reflect the graph of \(f(x)=x^3\) over the x-axis to graph \(h(x)=-x^3\). This means every point \((a, b)\) on the graph of \(f(x)=x^3\) will become \((a, -b)\) on the graph of \(h(x)=-x^3\). This will result in an inverted curvy 'S' that is in the second and fourth quadrants.

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