Question

what are the domain and range of this function?
y = |-3x - 18|
domain: all real numbers, range: all real numbers
domain: {x|x ≤ 0}, range: all real numbers
domain: {x|x ≤ 0}, range: {y|y ≥ 0}
domain: all real numbers, range: {y|y ≥ 0}

Explanation:

Step1: Analyze the Domain

The function is \( y = |-3x - 18| \). Absolute value functions have no restrictions on the input (x - values) because we can substitute any real number for \( x \) and still get a valid output. So the domain is all real numbers.

Step2: Analyze the Range

The absolute value of any real number is non - negative. That is, for any real number \( a \), \( |a| \geq 0 \). In the function \( y = |-3x - 18| \), let \( a=-3x - 18 \). Since \( x \) is any real number, \( a \) is also any real number, and \( y = |a| \geq 0 \). So the range is all real numbers \( y \) such that \( y\geq0 \), or \( \{y|y\geq0\} \).

Answer:

domain: all real numbers, range: \(\{y|y\geq0\}\) (the fourth option)