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

91影视

Precalculus Essentials

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

5 Edition

Chapter 2: 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

After entering the functions $f(x)=-x^{4}+2 x^{3}-6 x$ and $g(x)=-x^{4}$ on the graphing utility and using the $[\mathrm{ZOOMOUT}]$ feature, it becomes clear that both $f(x)$ and $g(x)$ show the same end behavior, they both tend downwards when $x$ approaches $-\infty$ or $+\infty$.

Step by step solution

Plotting the functions

Start by entering the functions $f(x)=-x^{4}+2 x^{3}-6 x$ and $g(x)=-x^{4}$ into the graphing calculator or graphing software. Make sure both functions show up in the graphing window.

Zoom Out

After plotting both functions, use the $[\mathrm{ZOOMOUT}]$ feature in the graphing tool. This will let you see how the functions behave when $x$ goes to $-\infty$ or $+\infty$.

Compare End Behavior

Observe the paths of $f(x)$ and $g(x)$. Even though they do not match completely, their end behavior (what the function approaches at $x$ values of extreme negative and positive) is the same. As $x$ approaches $-\infty$ or $+\infty$, both $f(x)$ and $g(x)$ tend downwards, thus displaying 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

Plotting the functions

Zoom Out

Compare End Behavior

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