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advanced-mathWhich statement about exponential functions is always true?
A
The domain is all real numbers
B
The range includes negative numbers
C
The graph has an x-intercept
D
The function is linear
Correct Answer: A
Choice A is the correct answer. Analyze properties of exponential functions.
- Domain: You can raise to any real power, so domain is all real numbers ✓
- Range: For and , output is always positive (no x-intercept).
- Shape: Exponential functions curve, not straight.
💡 Strategic Tip: Standard exponential (with ) never touches the x-axis.
Choice B is incorrect because for all when . Choice C is incorrect because the graph approaches but never reaches . Choice D is incorrect because exponential functions are not linear.