Question

Pre-calc, Which statement correctly uses limits to determine a vertical asymptote of _____ (image attached)

Answer 1

Option D

Explanation:

Given the function
`g(x)=(-7(x-5)^2(x+6))/((x-5)(x+5))`, we see that
`(x-5)` appears in both the numerator and denominator which cancel out to be
`(-7(x-5)(x+6))/((x+5))`. This means that there's a vertical asymptote at
`x=-5` for the denominator to be 0.

Additionally, the limit of the function g(x) as x approaches -5 from the left side is -∞. The limit of the function g(x) as x approaches -5 from the right side is ∞. See the attached graph for a visual of these limits.

In conclusion, option D is correct.