Answer :
Answer:- Horizontal Asymptote: y = 3
- Domain: all real numbers (x ∈ ℝ)
- Range: y ≥ 3, or [3, ∞)
Step-by-step explanation:The characteristics of the exponential function f(x) = 2^x + 3:
*Horizontal Asymptote:*
The horizontal asymptote is y = 3.
As x approaches negative infinity (−∞), the value of 2^x approaches 0, so the function approaches 3. As x approaches positive infinity (∞), the value of 2^x grows exponentially, but the function never touches the horizontal asymptote.
*Domain:*
The domain is all real numbers, x ∈ ℝ.
*Range:*
The range is y ≥ 3, or [3, ∞).
In other words:
- The function is defined for all real numbers (domain).
- The output values are always greater than or equal to 3 (range).
