Question

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

Answer 1

Answer:

Option D

Step-by-step explanation:

Given the function $g(x)=\frac{-7(x-5)^2(x+6)}{(x-5)(x+5)}$, we see that $(x-5)$ appears in both the numerator and denominator which cancel out to be $\frac{-7(x-5)(x+6)}{(x+5)}$. 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.