Advanced MathMediumLocation of the minimum of an absolute-value function
Advanced Math practice question
The function f is defined by f(x) = |2x − 6| + 5. For what value of x does f have its minimum value?
Answer: 3
|2x − 6| is never negative and equals 0 only when 2x − 6 = 0, that is, x = 3. There f(3) = 5, its minimum.
Common wrong answers
- If you answered 5
- 5 is the minimum value of f, not the x at which it occurs.
- If you answered 6
- 6 comes from 2x = 6 solved as x = 6, forgetting to divide by 2.
- If you answered -3
- −3 has the wrong sign: 2x − 6 = 0 gives x = 3.
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