9
advanced-math

Which statement about exponential functions y=abxy = ab^x 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.

  1. Domain: You can raise bb to any real power, so domain is all real numbers ✓
  2. Range: For a>0a > 0 and b>0b > 0, output is always positive (no x-intercept).
  3. Shape: Exponential functions curve, not straight.

💡 Strategic Tip: Standard exponential y=abxy = ab^x (with a,b>0a, b > 0) never touches the x-axis.

Choice B is incorrect becauseabx>0ab^x > 0 for all xx when a,b>0a, b > 0. Choice C is incorrect because the graph approaches but never reaches y=0y = 0. Choice D is incorrect because exponential functions are not linear.