Question

Determine the horizontal asymptote of the given function. If none exists, state that fact. 6x +1 g(x) = x2 – 64 O y = -8, y = 8 O no horizontal asymptotes Oy=6 O y = 0

Answer 1

Note these 2 points:

• If the degree of the numerator is BIGGER than degree of denominator, there is no horizontal asymptote

,

• If the degree of numerator is SMALLER than degree of denominator, the horizontal asymtote is the ,x-axis

,

• If the degree is numerator is EQUAL to degree of denominator, the equation of horizontal asymptote is y = a/b, where a is leading coefficient of numerator and b is leading coefficient of denominator

Now, looking at the equation, the degree of the numerator is SMALLER than the degree of the denominator. From above, point #2 holds.

The horizontal asymptote is the x-axis.

x-axis has the equation y = 0

The answer: y = 0