b. The function $f(x)=\frac{2 x^{2}+4 x-10}{2 x^{2}-x-13}$ has a horizontal asymptote at...
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Answer
Final Answer: The horizontal asymptote of the function \(f(x)=\frac{2 x^{2}+4 x-10}{2 x^{2}-x-13}\) is at \(y=\boxed{1}\).
Step 1 ：The horizontal asymptote of a rational function can be found by comparing the degrees of the numerator and denominator. If the degrees are the same, the horizontal asymptote is the ratio of the leading coefficients. In this case, the degrees of the numerator and denominator are both 2, and the leading coefficients are both 2.
Step 2 ：Therefore, the horizontal asymptote is at y = 2/2 = 1.
Step 3 ：Final Answer: The horizontal asymptote of the function \(f(x)=\frac{2 x^{2}+4 x-10}{2 x^{2}-x-13}\) is at \(y=\boxed{1}\).
