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

d

Explanation:

Answer 2

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

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.