+23251 I am assuming that you are trying to graph a rational function;
that is, a function of the type: f(x) = P(x) / Q(x).
Case 1: If the degree of P(x) is less than the degree of Q(x) then the graph as the x-axis as a horizontal asymptote.
Case 2: If the degree of P(x) is equal to the degree of Q(x), then the graph has an horizontal asymptote which is found by the equation; y = a / b where a is the leading coefficient of P(x) and b is the leading coefficient of Q(x).
The degree of a polynomial is the highest exponent of the variable.
Example of case 1: f(x) = (3x + 9) / (4x² - 14)
here the degree of P(x) = 1 and the degree of Q(x) = 2.
Example of case 2: f(x) = (7x³ -4x + 9) / (-x³ + x²) ---> asymptote is y = 7 / -1 ---> y = -7
In other cases, there will be no horizontal asymptote.
+23251 I am assuming that you are trying to graph a rational function;
that is, a function of the type: f(x) = P(x) / Q(x).
Case 1: If the degree of P(x) is less than the degree of Q(x) then the graph as the x-axis as a horizontal asymptote.
Case 2: If the degree of P(x) is equal to the degree of Q(x), then the graph has an horizontal asymptote which is found by the equation; y = a / b where a is the leading coefficient of P(x) and b is the leading coefficient of Q(x).
The degree of a polynomial is the highest exponent of the variable.
Example of case 1: f(x) = (3x + 9) / (4x² - 14)
here the degree of P(x) = 1 and the degree of Q(x) = 2.
Example of case 2: f(x) = (7x³ -4x + 9) / (-x³ + x²) ---> asymptote is y = 7 / -1 ---> y = -7
In other cases, there will be no horizontal asymptote.
+118658 Horizontal asymtotes are just the values that y cannot be but y can be some value infinitely close by.
You can look at the equation to see this.
ex
$$\\y+3=\frac{2}{x+1}\\\\
$I see straight off that $ \frac{2}{x+1}\ne 0\\\\
$therefore $ y+3\ne0 $ therefore $y\ne-3 \\\\
$y can be any value close to 3 but it cannot be 3. $ \\
$Therefore $
y=-3 $ is a horizontal asymptote. $$$
