2024 AMC 12A Problems/Problem 13
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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