1963 AMC 12 Problem 1

Attempt Problem 1 of the 1963 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1963 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

1.

Which one of the following points is not on the graph of y=xx+1?y=\dfrac{x}{x+1}?
(0,0)(0,0)
(−12,−1)\left(-\dfrac12,-1\right)
(12,13)\left(\dfrac12,\dfrac13\right)
(−1,1)(-1,1)
(−2,2)(-2,2)
Answer: D
Concepts:functionsubstitution
Small hint:
Check the domain before substituting coordinates
Big hint:
The denominator vanishes at one of the listed xx-coordinates
Solution:
The expression xx+1\frac{x}{x+1} is undefined when x=−1.x=-1. Therefore no point whose first coordinate is −1-1 can lie on its graph.
Thus, the correct answer is D.
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