How do i find the horizontal asymptote of h(x)=x+6/x^2-64 ?

I assume the equation described is:

( x + 6 ) / ( x^2 - 64 )

You can compare the degree of the numerator and denominator in a function that takes the form of this type of rational equation.

Here are the three rules

#1 (Correct Answer): When the degree of the numerator is smaller then the denominator the horizontal asymptote is y = 0

#2 If the degree of the numerator and denominator is the same, then you take the leading coefficient of the numerator (n) and denominator (d) to create the answer y = n / d in this equations case it would be 1 / 1 since variables technically have an invisible 1 in front of them since anything multiplied by 1 is its self, 1x = x

#3 When the degree of the numerator is greater then the degree of the denominator then this means that it does not have a horizontal asymptote.

Again the final answer is that the horizontal asymptote is y = 0

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.