Question

Describe how the following absolute value function is transformed from the parent function y = |x|:

y = 4x - 51 - 6
A. The graph is vertically stretched, shifted left 5 units, and shifted down 6 units.
B. The graph is vertically stretched, shifted right 5 units, and shifted down 6 units.
C. The graph is vertically compressed, shifted left 5 units, and shifted down 6 units.
D. The graph is vertically compressed, shifted right 5 units, and shifted down 6 units.

Answer 1

The absolute value function y = 4|x - 12.75| - 6 represents a vertical stretch by a factor of 4, a horizontal shift to the right by 12.75 units, and a vertical shift downward by 6 units.

Step-by-step explanation:

To determine how the given absolute value function y = 4|x - 12.75| - 6 is transformed from the parent function y = |x|, we need to consider the effect of each operation on the graph of the function. The coefficient 4 in front of the absolute value term indicates a vertical stretch by a factor of 4.

Next, the expression inside the absolute value is x - 12.75, which can be rewritten as x - 51/4. This moves the graph horizontally to the right by 12.75 or 51/4 units, since the absolute value function shifts to the right by the amount that x is translated inside the absolute value.

Lastly, the -6 at the end of the expression shows that the graph is moved vertically downward in the coordinate system by 6 units. Therefore, the transformation of the function is a vertical stretch by a factor of 4, a horizontal shift to the right by 12.75 units (or equivalently, 51/4 units), and a vertical shift downward by 6 units.