Look at this example
f(x) = 6x2 + x + 43x2 + 5
Numerator degree
2
2
Denominator degree
2
2
Leading coefficient on top: 6
Leading coefficient on bottom: 3
Leading coefficient on bottom: 3
Horizontal Asymptote · Equal Degrees
“The highest power is 2 on top and 2 on the bottom.
The degrees are equal. What do I do?”
The degrees are equal. What do I do?”
“I divide the leading coefficients:
leading coefficient of the numeratorleading coefficient of the denominator
Top gives 6. Bottom gives 3.”63= 2→y = 2
“My horizontal asymptote is y = 2.”
Equal degrees → divide the leading coefficients → write y = the result.
Watch the thinking bubbles.