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To find out end behavior, we always look at the largest exponent (3 in this case) and the sign of the term with the largest exponent (negative in this case). We can rule out the first two choices because since it is a cubic graph (exponent of 3) the graph will be pointing in opposite directions. Then, the negative tells us that as the x values approache infinity, the y values will approach negative infinity. So the correct answer is the last choice.

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The fourth option is correct because the fourth graph has the same end behavior as the given function.

Given:

The given function is:

[tex]f(x)=-3x^3-x^2+1[/tex]

To find:

The graph that has the same end behavior as the given function.

Explanation:

We have,

[tex]f(x)=-3x^3-x^2+1[/tex]

Here, the leading coefficent is [tex]-3[/tex] and the degree of the function is [tex]3[/tex].

Since the leading coefficent is negative and the degree is an odd number, therefore,

[tex]f(x)\to \infty[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to \infty[/tex]

End behavior of first graph:

[tex]f(x)\to \infty[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to \infty[/tex] as [tex]x\to \infty[/tex]

End behavior of second graph:

[tex]f(x)\to -\infty[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to \infty[/tex]

End behavior of third graph:

[tex]f(x)\to -\infty[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to \infty[/tex] as [tex]x\to \infty[/tex]

End behavior of fourth graph:

[tex]f(x)\to \infty[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to \infty[/tex]

Therefore, the fourth option is correct.

Learn more:

https://brainly.com/question/11845052

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