Question

The parent function is y = |2|. Describe all of the transformations needed to graph y = 2(x + 2)?

A. Vertical compression by a factor of 2 and down 2 units
B. Reflect over the x-axis, vertical stretch by a factor of 2 and left 2 units
C. Vertical stretch by a factor of 2 and left 2 units
D. Reflect over the x-axis, vertical stretch by a factor of 2 and right 2 units
E. Vertical stretch by a factor of 2 and up 2 units
F. Vertical compression by a factor of 2 and right 2 units

Answer 1

To graph y = 2(x + 2) from the parent function y = |2|, we need a vertical stretch by a factor of 2 and a horizontal translation 2 units to the left. Thus correct option is C.

Step-by-step explanation:

The student is asked to describe the transformations needed to graph the function y = 2(x + 2) from the parent function y = |2|. The correct transformations are:

A vertical stretch by a factor of 2. This is because the coefficient in front of the (x + 2) term is 2, which stretches the graph vertically.

A horizontal translation 2 units to the left. This is indicated by the (x + 2) inside the function, which means that every x value in the parent function is decreased by 2, shifting the graph leftward.

Therefore, the correct answer to the student's question is C. Vertical stretch by a factor of 2 and left 2 units.