SOLUTION: State the horizontal asymptote of the rational function. For full credit, explain the reasoning you used to find the horizontal asymptote. f(x) = quantity x plus nine divided by

Question 1100958: State the horizontal asymptote of the rational function. For full credit, explain the reasoning you used to find the horizontal asymptote.
f(x) = quantity x plus nine divided by quantity x squared plus four x plus two
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The rational function is

The degree of the denominator is larger than the degree of the numerator. That means that, for large positive or large negative values, the denominator gets big faster than the numerator; therefore the function value gets closer to zero.

So the function has a horizontal asymptote of y=0.

Note that the function value is 0 at x=9.

That means the graph crosses the horizontal asymptote at that point.

As x gets very large positive, the function value is a small positive number; as x gets very large negative, the function value is a small negative number.
RELATED QUESTIONS
State the horizontal asymptote of the rational function. For full credit, explain the... (answered by algebrahouse.com,josgarithmetic)

State the horizontal asymptote of the rational function. For full credit, explain the... (answered by josgarithmetic)

sketch the graph of each rational function: 3x - 4 / 10x^2 - 21x - 10 find vert.... (answered by solver91311)

Find the exact value of tan [arcsin (2/5)]. For full credit, explain your reasoning. (answered by ikleyn)

Find the exact value of cos(arcsin(one fourth)). For full credit, explain your reasoning. (answered by stanbon)

Please explain in words how to determine the equation of the horizontal asymptote for the (answered by solver91311)

State the horizontal asymptote of the rational function. f(x) = 5x+1/9x-2 (answered by ikleyn)

State the horizontal asymptote of the rational function. f(x) = (5x+1)/(9x-2) (answered by josgarithmetic)

Find the horizontal asymptote of the rational function... (answered by Nate)