Problem 99 Use a graphing utility to graph ... [FREE SOLUTION]

Chapter 3: Problem 99

Use a graphing utility to graph $f$ and $g$ in the same viewing rectangle. Then use the $[\mathrm{ZOOMOUT}]$ feature to show that $f$ and $g$ have identical end behavior. $$f(x)=-x^{4}+2 x^{3}-6 x, \quad g(x)=-x^{4}$$

Short Answer

Expert verified

Upon using a graphing utility to graph the functions $f(x) = -x^{4} + 2x^{3} - 6x$ and $g(x) = -x^{4}$, and using ZOOMOUT feature, it clearly shows that both functions have identical end behavior. As $x$ approaches positive or negative infinity, both function graphs move towards negative infinity.

Step by step solution

Graph the functions

Using a graphing utility or calculator, input the functions $f(x) = -x^{4} + 2x^{3} - 6x$ and $g(x) = -x^{4}$. Graph the functions in the same viewing rectangle.

Use ZOOMOUT Feature

Once the functions are graphed, use the ZOOMOUT feature on the graphing utility. This will make the graph smaller and allow you to observe the end behavior of the functions.

Analyze the end behavior

Observe the graphs of both functions. Notice how they have the same end behavior. As $x$ approaches positive or negative infinity, both function graphs move towards negative infinity, indicating that they have identical end behavior.

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91影视

Use a graphing utility to graph \(f\) and \(g\) in the same viewing rectangle. Then use the \([\mathrm{ZOOMOUT}]\) feature to show that \(f\) and \(g\) have identical end behavior. $$f(x)=-x^{4}+2 x^{3}-6 x, \quad g(x)=-x^{4}$$

Short Answer

Step by step solution

Graph the functions

Use ZOOMOUT Feature

Analyze the end behavior

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