AnswersPrecalculusUnderstanding the Concept of a LimitQuestion 8
8
QuizMultiple Choice

Understanding the Concept of a Limit

Question 8 • Precalculus

Review the table of values for function h(x).xh(x)8.93.838.99–1.198.9994.739undefined9.001–4.739.011.199.1–3.83

Answer
A
The limit does not exist because the values of h(x) seem to oscillate between random values around x = 9.
B
The limit does exist because h(x) is defined for all given values around x = 9, even though h(x) isn’t defined at x = 9.
C
The limit does not exist because h(x) is not defined at x = 9, and for a limit to exist, the function must be defined at x = 9.
D
The limit does exist because the values of h(x) to the right of x = 9 are all opposites of the values of h(x) to the left of x = 9.

Explanation

As x gets close to 9, the listed h(x) values do not settle toward one number; they vary between positive and negative values, such as 4.739 and −4.739. A limit exists only if the function values approach the same single number from both sides. Whether h(9) is defined does not determine whether the limit exists, so the explanation in choice C is incorrect.

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