Which of the following describes the transformation of g (x) = 3 (2) superscript negative x baseline + 2 from the parent function f (x) = 2 superscript x?
reflect across the x-axis, stretch the graph vertically by a factor of 3, shift 2 units up
reflect across the y-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the x-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up

Option d: reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.

Step-by-step explanation:

The parent function is

The transformation function is

In the transformed function, the function is added +2, which shifts the graph by 2 units up.

Also, the function is multiplied by 3, which stretches the function  vertically by a factor of 3 units.

The variable x is multiplied by -1, such that the function reflects across y-axis.

Thus, the correct answer is option d.

The graph is attached below which shows the parent function and the transformed function.

The transformation function is reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.

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