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advanced-mathThe graph of has a horizontal asymptote at . Which must be true?
A
and no vertical shift
B
C
D
The graph is a horizontal line
Correct Answer: A
Choice A is the correct answer. Identify conditions for asymptote at .
- Standard Form: has asymptote at (x-axis).
- Shifted Form: has asymptote at .
- Condition: For asymptote at , there must be no vertical shift () and .
💡 Strategic Tip: Basic exponential always approaches as (depending on ).
Choice B is incorrect because if , the function would be (constant). Choice C is incorrect because must be positive in exponential functions. Choice D is incorrect because exponential graphs curve, not flat.