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Step-by-step explanation:
End behavior of a polynomial function is the behavior of the graph of f(x) as x tends towards infinity in the positive or negative sense.
Given function:
f(x) = 2x⁶ - 2x² - 5
To find the end behavior of a function:
- Find the degree of the function. it is the highest power of the variable.
Here the highest power is 6
- Find the value of the leading coefficient. It is the number before the variable with the highest power.
Here it is +2
We observe that the degree of the function is even
Also the leading coefficient is positive.
For even degree and positive leading coefficient, the end behavior of a graph is:
x → ∞ , f(x) = +∞
x → -∞ , f(x) = +∞
The graph is similar to the attached image
Learn more:
End behavior brainly.com/question/3097531
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