Question

the value of the absolute value function \\(y = |x|\\) is always ______.

a. negative
b. zero
c. positive

Explanation:

Analyze the absolute value function

The absolute value function is defined as:

$$ y = |x| =
LATEXBLOCK0
$$

This operation outputs the non-negative distance of a number from zero.

Evaluate the range of the function

For any real number input \(x\), the output value \(y = |x|\) is always greater than or equal to zero:

$$ |x| \ge 0 $$

This means the output values are non-negative.

Match with the given options

Let's evaluate the provided choices:

• a. negative: Incorrect, as absolute value is never negative.
• b. zero: Incorrect, as it is only zero when \(x = 0\), but positive for all other values.
• c. positive: This is the best fit among the choices, as the output is non-negative (positive or zero).

Answer:

• a. negative
• b. zero
• c. positive (Correct answer)