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What is the range of this function?\newliney = |x|\newlineChoices:\newlineall real numbers\text{all real numbers}\newline{y∣y≥0}\{y \mid y \geq 0\}\newline{y∣y≤0}\{y \mid y \leq 0\}\newline{y∣y>0}\{y \mid y > 0\}

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Domain and range of absolute value functions: equationsright chevron icon

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Q. What is the range of this function?\newliney = |x|\newlineChoices:\newlineall real numbers\text{all real numbers}\newline{y∣y≥0}\{y \mid y \geq 0\}\newline{y∣y≤0}\{y \mid y \leq 0\}\newline{y∣y>0}\{y \mid y > 0\}
  1. Define Range of Function: The range of a function is the set of all possible output values (yy-values) that the function can produce. We need to determine what values yy can take when y=∣x∣y = |x|.
  2. Absolute Value Function Output: The absolute value function |x|\
  3. Minimum Value of \(y: Since ∣x∣|x| is always non-negative, the smallest value yy can take is 00. There is no upper limit to the values of yy because xx can be any real number, and the absolute value of any real number is also a real number.
  4. Range of Function: Therefore, the range of the function y=∣x∣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}\{y | y \geq 0\}.

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