The range of the function $f(x) = x^{2}$ for $x \in \{-4, -3, -2, -1, 0, 1, 2, 3, 4\}$ is:
A$\{-16, -9, -4, -1, 0, 1, 4, 9, 16\}$
B$\{16\}$
C$\{0, 1, 2, 3, 4\}$
D$\{0, 1, 4, 9, 16\}$
Answer & Solution
Correct answer: D. $\{0, 1, 4, 9, 16\}$
Squaring: $(\pm 1)^{2} = 1$, $(\pm 2)^{2} = 4$, $(\pm 3)^{2} = 9$, $(\pm 4)^{2} = 16$, $0^{2} = 0$. The output set is $\{0, 1, 4, 9, 16\}$ — squaring collapses $\pm x$ to the same value.
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