Pre-calc, Which statement correctly uses limits to determine a vertical asymptote of _____ (image attached)
1 answer:
Answer:
Option D
Step-by-step explanation:
Given the function , we see that
appears in both the numerator and denominator which cancel out to be
. This means that there's a vertical asymptote at
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.
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Answer: Choice C.
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Explanation:
The domain is the set of all allowed x inputs.
Here we see that x = -3 is the smallest x value possible as it is from the left-most point. The graph goes on forever to the right, so there is no largest x value. Effectively infinity is the largest x value even though infinity is not a number.
We can say the domain is which can be simplified to
or
In short: x can be -3 or larger.