Advanced MathVery hardInput shift as an output factor
Advanced Math practice question
For the functions f(x) = 2ˣ and g(x) = f(x + 3), g(x) = k · f(x) for every x. What is the value of k?
Answer: 8
g(x) = 2ˣ⁺³ = 2³ · 2ˣ = 8 · f(x), so k = 8.
Common wrong answers
- If you answered 2
- Each unit of shift contributes one factor of 2; three units give 8.
- If you answered 3
- The shift of 3 becomes the factor 2³ = 8.
- If you answered 6
- 6 is 2 · 3; the factor is 2 raised to the 3rd power.
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