The horizontal asymptote is y=-0.5.
How to find horizontal asymptote?
If the degree of the polynomial in the numerator and the denominator is same then the horizontal asymptote is given by [tex]y=\frac{\text{leading coefficient of the numerator}}{\text{ leading coefficient of the denominator}}[/tex]
What will the horizontal asymptote of given function?
In the given function, the degree of the polynomial of the numerator is 2 and of the denominator is also 2.
The leading coefficient in the numerator is -5 and in the denominator it is 10.
Divide -5 by 10 and equate the result to y to get the horizontal asymptote .
[tex]y=\frac{-5}{10}[/tex]
y=-0.5
Therefore, the correct option is b.
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