Questions: Draw a quick sketch of the equation. y = sqrt(-9x)

Solution Steps

The given equation is \( y = \sqrt{-9x} \). This is a square root function, and the expression inside the square root must be non-negative for real values of \( y \).

For \( y = \sqrt{-9x} \) to be defined, the expression inside the square root must be non-negative: \[ -9x \geq 0 \] \[ x \leq 0 \] Thus, the domain of the function is \( x \leq 0 \).

Since \( y = \sqrt{-9x} \), we can rewrite it as: \[ y = \sqrt{9(-x)} \] \[ y = 3\sqrt{-x} \] This indicates that as \( x \) becomes more negative, \( y \) increases. The function is only defined for \( x \leq 0 \) and \( y \geq 0 \).

The correct graph should:

• Be defined only for \( x \leq 0 \)
• Show \( y \) increasing as \( x \) becomes more negative

Final Answer