1955 AMC 12 Problem 28
Attempt Problem 28 of the 1955 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 1955 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
On the same set of axes are drawn the graph of and the graph of the equation obtained by replacing by in the given equation. If and these two graphs intersect:
in two points, one on the -axis and one on the
-axis
in one point located on neither axis
only at the origin
in one point on the -axis
in one point on the -axis
Answer: E
Small hint:
The reflected graph is
Big hint:
Set the two expressions for equal and use
Solution:
Replacing by gives At an intersection, so Since we must have and then There is exactly one intersection, on the -axis.
Thus, the correct answer is E.
Problem 28 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
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