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)?
- A. f(x) > 1Correct
- B. f(x) ≥ 1
- C. f(x) > 0
- 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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