2024 AMC 12A Problems/Problem 13
Problem
The graph of has an axis of symmetry. What is the reflection of the point
over this axis?
Solution 1
The line of symmetry is probably of the form for some constant
. A vertical line of symmetry at
for a function
exists if and only if
; we substitute
and
into our given function and see that we must have
for all real . Simplifying:
If , then
for all real
; this is clearly impossible, so let
. Thus, our line of symmetry is
, and reflecting
over this line gives
~Technodoggo
See also
2024 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.