Question

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

Answer 1

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 $f(x)=2^{x}$

The transformation function is $g(x)=3(2)^{-x} +2$

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 $f(x)=2^{x}$  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.

Answer 2

Answer:

d

Step-by-step explanation: