Question

Identify the vertical and or horizontal asymptotes for each function y=5x/x-1

Answer 1

y=5x/(x-1)

To get the vertical asymptote, set the denominator equal to 0 and solve for x.

x - 1 = 0
x = 1 which is a vertical line passing through the point (1,0) and perpendicular to the x-axis. The graph of the function does not intersect the vertical asymptote.

Answer 2

To get the horizontal asymptote, take the dominant term of the numerator, 5x, and divide by the dominant term of the denominator, x.

5x/x = 5 and the equation of the horizontal asymptote is y = 5.