For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1?​

for a rational expression the vertical asymptotes occur when the denominator equals 0, in this case that will be when x + a = 0.now, if there were to be a vertical asymptote of x = 1, that simply means that x = 1 ==> x - 1 = 0.meaning that a = -1.horizontal asymptotes occur when the denominator has a higher degree than the numerator OR when both have the same degree.when the degree of the denominator is higher, then the only horizontal asymptote occurring is y = 0.when the degrees are the same, then the horizontal asymptote occurs at the leading terms' coefficient fraction.now, if this expression were to have a horizontal asymptote of y = 2, that simply means[tex]\bf \cfrac{2x^m}{x+a}\implies \cfrac{2x^1}{1x^1+a}\implies \stackrel{\textit{horizontal asymptote}}{\cfrac{2}{1}\implies y=2}\qquad \textit{meaning m = 1}[/tex]