2008 AMC 12A Problems/Problem 12
Contents
Problem
A function has domain
and range
. (The notation
denotes
.) What are the domain and range, respectively, of the function
defined by
?
Solution
is defined if
is defined. Thus the domain is all
.
Since ,
. Thus
is the range of
.
Thus the answer is .
Solution 2
Look at the vertical and horizontal translations, and we rewrite the function to a more recognizable to help us visualize.
Horizontal: There is one horizontal shift one unit to the left from the component making the domain
Vertical: There is one vertical mirror from the
causing the range to become
and then a vertical shift one unit upward from the
causing the range to become
.
This generates the answer of \longrightarrow \boxed{B}$.
~PhysicsDolphin
See Also
2008 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 11 |
Followed by Problem 13 |
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 |
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