What is the range of this function? y = |x| Choices: [[all real numbers][{y | y ≥ 0}][{y | y ≤ 0}][{y | y > 0}]]

Define Range of Function: The range of a function is the set of all possible output values (y-values) that the function can produce. We need to determine what values y can take when y = |x|.Absolute Value Function Output: The absolute value function |x| outputs the non-negative value of x. This means that for any real number x, |x| is always greater than or equal to zero.Minimum Value of y: Since |x| is always non-negative, the smallest value y can take is 0. There is no upper limit to the values of y because x can be any real number, and the absolute value of any real number is also a real number.Range of Function: Therefore, the range of the function y = |x| includes all real numbers that are greater than or equal to zero. This can be written in set notation as {y | y ≥ 0}.

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What is the range of this function? $\newline$ y = |x| $\newline$ Choices: $\newline$ $\text{all real numbers}$ $\newline$ $\{y \mid y \geq 0\}$ $\newline$ $\{y \mid y \leq 0\}$ $\newline$ \{y \mid y > 0\}

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Algebra 2

Domain and range of absolute value functions: equations

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Q. What is the range of this function?

\newline

y = |x|

\newline

Choices:

\newline

\text{all real numbers}

\newline

\{y \mid y \geq 0\}

\newline

\{y \mid y \leq 0\}

\newline

\{y \mid y > 0\}

Define Range of Function: The range of a function is the set of all possible output values ( $y$ -values) that the function can produce. We need to determine what values $y$ can take when $y = |x|$ .
Absolute Value Function Output: The absolute value function |x|\
Minimum Value of \(y: Since $|x|$ is always non-negative, the smallest value $y$ can take is $0$ . There is no upper limit to the values of $y$ because $x$ can be any real number, and the absolute value of any real number is also a real number.
Range of Function: Therefore, the range of the function $y = |x|$ includes all real numbers that are greater than or equal to zero. This can be written in set notation as $\{y | y \geq 0\}$ .