Sketch the graph of the rational function .

Question

Sketch the graph of the rational function  .

Quizplus · Accepted Answer

- The function has a vertical asymptote at x=2 because a factor (x-2) is in the denominator but not in the numerator.
- The function has a horizontal asymptote at y=0 because the highest degree of x in the denominator and numerator is the same and equal to 1.
- The function goes through the point (-1,0) because plugging in x=-1 gives a numerator value of 0, and the denominator is non-zero.
- The function is positive for large negative values of x and negative for large positive values of x because as x approaches negative infinity, the function approaches the horizontal asymptote from above, and as x approaches positive infinity, the function approaches the horizontal asymptote from below.

Sketch the Graph of the Rational Function