Question

Determine the transformations of g(x)=12|x+5|+6 if the parent function is f(x)=|x|.

Answer 1

The function g(x)=12|x+5|+6 is the result of the parent function f(x)=|x| being horizontally shifted 5 units to the left, vertically stretched by a factor of 12, and vertically shifted upwards by 6 units.

Step-by-step explanation:

The question involves understanding the transformations of the function g(x)=12|x+5|+6 given that the parent function is f(x)=|x|. To determine the transformations, we compare the two functions. The function g(x) can be viewed as the parent function f(x) having undergone a horizontal shift left by 5 units, a vertical stretch by a factor of 12, and a vertical shift upwards by 6 units.

Step-by-step explanation:

1. Identify the horizontal shift: The |x+5| inside the absolute value indicates a horizontal shift. Since it is x + 5, the shift is 5 units to the left.
2. Identify the vertical stretch: The coefficient of 12 in front of the absolute value represents a vertical stretch by a factor of 12.
3. Identify the vertical shift: The +6 outside the absolute value indicates a vertical shift upward by 6 units.

These transformations change the shape and position of the graph of the parent function on the coordinate plane.