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Which graph has the same end behavior as the graph of f(x)=x⁴+x³-x²-x

Sagot :

Using limits, a graph that goes to positive infinity when [tex]x = -\infty[/tex] and [tex]x  = \infty[/tex] would have the same end behavior as the function [tex]f(x) = x^4 + x^3 - x^2 - x[/tex].

What is the end behavior of a function?

It is given by it's limits as x goes to negative and positive infinity.

In this problem, the function is:

[tex]f(x) = x^4 + x^3 - x^2 - x[/tex]

The limits are:

  • [tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} x^4 + x^3 - x^2 - x = \lim_{x \rightarrow -\infty} x^4 = (-\infty)^4 = \infty[/tex].
  • [tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} x^4 + x^3 - x^2 - x = \lim_{x \rightarrow \infty} x^4 = (\infty)^4 = \infty[/tex].

A graph that goes to positive infinity when [tex]x = -\infty[/tex] and [tex]x  = \infty[/tex] would have the same end behavior as the function [tex]f(x) = x^4 + x^3 - x^2 - x[/tex].

More can be learned about limits and end behavior at https://brainly.com/question/27830331

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