The horizontal asymptote of the function h(x)= -x^2+5x-2/x^2+2 is -1.
The line y = a is horizontal asymptote if the function f(x) tends to 'a' from upside of that line y = a, or from downside of that line.
Horizontal Asymptote is when the function f(x) is tending to zero for x = +∞ and x = - ∞
The given function is;
h(x)= -x^2+5x-2/x^2+2
Let the rational function f(x) = mx^a / mx^b where and a and b are degree of numerator and denominator.
If a < b , then y axis y = 0 is a horizontal asymptote.
If b = a then horizontal asymptote is the line y = p/q
Here, the value is b = 2 and a = 2
Since b = a the horizontal asymptote is the line
y = m/n where m = -1 and n = 1
Therefore y = -1
Horizontal asymptotes y = -1.
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