Answer :
The horizontal asymptotes of f(x) are y = 0.
Given function is
f(x) = 2x¹² - 5x²0 - 1520x20 + 7x8 - 54
There is no common factor to remove.To find horizontal asymptotes, determine the highest power of x in the numerator and the denominator.
Here, the highest power of x in the numerator is 20x²0.
The highest power of x in the denominator is also 20x²0.
To find the horizontal asymptote, divide the coefficient of the highest power of x in the numerator by the coefficient of the highest power of x in the denominator which is (2/20) = (1/10).
Therefore, the horizontal asymptotes of f(x) are y = 0.
Horizontal asymptote is a horizontal line that a curve approaches as x (input of the function) tends to +∞ or -∞ (the two infinities).
This line is a horizontal asymptote if, as x becomes very large or very small, the y-value (output) of the function approaches a constant value in the long run.
To find horizontal asymptotes, determine the highest power of x in the numerator and the denominator. Here, the highest power of x in the numerator is 20x²0.
The highest power of x in the denominator is also 20x²0.
To find the horizontal asymptote, divide the coefficient of the highest power of x in the numerator by the coefficient of the highest power of x in the denominator which is (2/20) = (1/10).
Therefore, the horizontal asymptotes of f(x) are y = 0.
To learn more about horizontal line
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