Question

describe the transformations that maps ( y = g(x + 6) - 10 )
options:
reflect over x-axis
shifted down 10 units
shifted left 6 units

reflect over y-axis
shifted up 10 units
shifted right 6 units

reflect over x-axis
shifted up 10 units
shifted left 6 units

reflect over y-axis
shifted down 10 units
shifted left 6 units

Explanation:

Step1: Identify x-axis reflection

The negative sign outside $g(x+6)$ ($-g(x+6)$) reflects the graph of $g(x)$ over the x-axis.

Step2: Identify horizontal shift

The $x+6$ inside the function $g(x+6)$ shifts the graph of $g(x)$ left 6 units.

Step3: Identify vertical shift

The $-10$ outside the reflected and shifted function shifts the graph down 10 units.

Answer:

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units