Question

9 select the transformations of $g(x) = -2|x - 6|$ as it relates to the parent function. a vertical compression b vertical stretch c reflected over x - axis d translated down 6 units e translated right 6 units f translated left 6 units

Explanation:

Step1: Identify parent function

The parent function of \(g(x)\) is \(f(x) = |x|\).

Step2: Analyze vertical transformation

The coefficient \(-2\) outside the absolute value:

• The negative sign reflects the graph over the x-axis.
• Since \(|-2| > 1\), this creates a vertical stretch.

Step3: Analyze horizontal transformation

The term \(x - 6\) inside the absolute value means the graph is translated right 6 units (for \(|x - h|\), \(h>0\) shifts right).

Answer:

B. Vertical stretch
C. Reflected over x-axis
E. Translated right 6 units