0The exponent of the power function is 9 (an odd number). Because the coefficient is –1 (negative), the graph is the reflection about the x-axis of the graph of f(x)=x9f(x)=x9. Figure 3.3.63.3.6shows that as xx approaches infinity, the output decreases without bound. As xx approaches negative infinity, the output increases without bound. In symbolic form, we would write
as x→−→−∞,f(x)→→∞as x→→∞,f(x)→−→−∞as x→−→−∞,f(x)→→∞as x→→∞,f(x)→−→−∞
Figure 3.3.63.3.6: Graph of f(x)=−x9f(x)=−x9.
Analysis
We can check our work by using the table feature on a graphing utility.
