Consider the following function. f(x) = 1/x – 8

Question

Determine whether f(x) approaches ∞ or -∞ as x approaches 8 from the left and from the right.

Answer 1

f(x) = 1/(x-8)

as x approaches 8 from the left, from 7.5, 7.6, 7.7, 7.8, 7.9, closer & closer to 8, f(x) approaches negative infinity.

as x approaches 8 from the right, from 8.9, 8.8, 8.7, 8.6, 8.5, 8.4, 8.3, 8.2, 8.1, closer and closer to 8, f(x) approaches positive infinity

if you graph f(x), it's a rectangular hyperbola with vertical asymptote x= 8 and y = horizontal asymptote y = -1/8. the graph has two separate branches, one mostly in quadrant I, and the other in quadrant III & IV.

UNLESS, by chance you really meant f(x) =1/x -8, then as x approaches 8 from left or right, f(x) approaches 1/8 - 8 = 7.875