Advanced MathMediumSymmetry of an absolute-value function
Advanced Math practice question
The function g is defined by g(x) = |x − a|, where a is a constant. If g(2) = g(10), what is the value of a?
Answer: 6
|x − a| is symmetric about x = a, so equal outputs at 2 and 10 mean a is midway: a = (2 + 10)/2 = 6.
Common wrong answers
- If you answered 4
- 4 is half of 8, the distance from a to each input, not a itself.
- If you answered 8
- 8 is 10 − 2, the distance between the inputs.
- If you answered 12
- 12 is 2 + 10, forgetting to halve.
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