Answered

IDNLearn.com offers expert insights and community wisdom to answer your queries. Whether it's a simple query or a complex problem, our community has the answers you need.

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

Precalc Which Statement Correctly Uses Limits To Determine A Vertical Asymptote Of Image Attached class=

Sagot :

Answer:

Option D

Step-by-step explanation:

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

View image Goddessboi
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.