Question

Which description of transformations yields the

equation () = | - 1| +3 from its parent function
of () = ||?
A) shift right 1 units and up 3 units
B) shift left 1 units and up 3 units
C) shift right 1 units and down 3 units
D) shift left 1 units and down 3 units

Answer 1

The equation f(x) = |x - 1| + 3 indicates a horizontal shift to the right by 1 unit and a vertical shift upward by 3 units from the parent function f(x) = |x|.

Step-by-step explanation:

The equation f(x) = |x - 1| + 3 is derived from its parent function f(x) = |x| by applying specific transformations. To determine the correct transformations, we need to analyze the changes made to the parent function. The term - 1 inside the absolute value indicates a horizontal shift to the right side of the coordinate system by 1 unit since we subtract 1 from x. Meanwhile, the + 3 outside the absolute value denotes a vertical shift upward in the coordinate system by 3 units. So the correct description of transformations would be:

• Shift right 1 unit.
• Shift upward 3 units.

Therefore, the correct answer is A) shift right 1 units and up 3 units.