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(A) The ranges of the given functions are as follows:$1$. For $f(x) = |x|$,the output is always non-negative,so the range is $[0, \infty)$. Thus,$A-I$

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(A) The ranges of the given functions are as follows:$1$. For $f(x) = |x|$,the output is always non-negative,so the range is $[0, \infty)$. Thus,$A-I$ or $A-III$.$2$. For $f(x) = x^2$,the output is always non-negative,so the range is $[0, \infty)$. Thus,$B-I$ or $B-III$.$3$. For $f(x) = x^3$,the function covers all real values,so the range is $\mathbb{R}$. Thus,$C-II$.$4$. For $f(x) = 	ext{sgn}(x)$,the signum function outputs $-1$ for $x  0$. Thus,the range is $\{-1, 0, 1\}$. Thus,$D-IV$.

Function	Range
$A. f(x) = \|x\|$	$I. [0, \infty)$
$B. f(x) = x^2$	$II. \mathbb{R}$
$C. f(x) = x^3$	$III. [0, \infty)$
$D. f(x) = \text{sgn}(x)$	$IV. \{-1, 0, 1\}$

Match the following functions with their respective ranges:
Function Range
$A. f(x) = |x|$ $I. [0, \infty)$
$B. f(x) = x^2$ $II. \mathbb{R}$
$C. f(x) = x^3$ $III. [0, \infty)$
$D. f(x) = \text{sgn}(x)$ $IV. \{-1, 0, 1\}$

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Match the following functions with their respective ranges:FunctionRange$A. f(x) = |x|$$I. [0, \infty)$$B. f(x) = x^2$$II. \mathbb{R}$$C. f(x) = x^3$$III. [0, \infty)$$D. f(x) = \text{sgn}(x)$$IV. \{-1, 0, 1\}$