Question

Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function f(x) = |x|. The vertex is (Type an ordered pair). The axis of symmetry is x=0. What are the transformations from the parent function?

A) The function is translated 6 units to the right and 4 units down.
B) The function is translated 4 units to the right and 6 units down.
C) The function is translated 6 units up and vertically stretched by a factor of 4.
D) The function is translated 6 units to the left and 4 units down.
E) The function is translated 6 units to the right and vertically stretched by a factor of 4.
F) The function is translated 4 units down and vertically stretched by a factor of 6.

Answer 1

The vertex for the transformed function from f(x) = |x| that is translated 6 units right and 4 units down is (6, -4), and the axis of symmetry is x = 6.

Step-by-step explanation:

To identify the vertex, axis of symmetry, and transformations of a function transformed from the parent function f(x) = |x|, one has to understand how algebraic manipulations relate to geometric transformations on the coordinate system. The given options suggest translations and stretches as possible transformations.

Option A implies translation c. Horizontally to the right side of the coordinate system by 6 units and b. Vertically downward in the coordinate system by 4 units. To represent these transformations in algebraic terms, the function would take on the form f(x) = |x - 6| - 4. This indicates that the vertex of the transformed function is at (6, -4) and the axis of symmetry would be x = 6.