How do you solve this?

Question

consider the function f(x) = 6 / e^(-5x)-6

What is the horizontal asymptote to the left? to the right?
What is the vertical asymptote?

Answer 1

To find the asymptote to the left. find the limit of f(x) as x approaches -∞.

To find the asymptote to the right. find the limit of f(x) as x approaches ∞.

Vertical asymptotes usually occur where a value of x gives a division by zero. Find when the denominator equals zero then take the limit as x approches that value to make sure the value of the function approaches negative or positive infinity.

I hope that helps.

Answer 2

As +x gets large, e^-(5x) gets very small comoared to 6, so the horizontal asymptote to the right (positive x) is 6/-6 = -1; As x get to large negative values, e^-(5x) gets very big compared to 6, and the equation becomes 6/e-(5x); for large negative x, this approaches 0. When e^-(5x) approaches 6, the equation approaches ∞ as a vertical asymptote. This occurs as -5x = ln(6), or x->ln(6) / 5. The vertical asymptote is the vertical line through x = ln(6) / 5. Finding asymptotes is made easier by graphing the function on a graphing calculator or use this site: http://www.coolmath.com/graphit/index.html