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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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