16Hit1600
Advanced MathVery hardRange of a shifted exponential

Advanced Math practice question

The function f is defined by f(x) = 2ˣ + 1. Which of the following describes all possible values of f(x)?

  1. A. f(x) > 1Correct
  2. B. f(x) ≥ 1
  3. C. f(x) > 0
  4. D. All real numbers

Answer: A. f(x) > 1

2ˣ is always positive and can be made as small as you like, but never reaches 0. So 2ˣ + 1 takes every value greater than 1, but never 1 itself.

Why the other answers are wrong

B. f(x) ≥ 1
f(x) never actually equals 1, because 2ˣ never equals 0.
C. f(x) > 0
Values between 0 and 1 are never reached: 2ˣ + 1 is always more than 1.
D. All real numbers
Negative values and values below 1 are never reached.

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