Question

which if the following describes the transformations of g(x)=-(2)^x+4 -2 from the parent function f(x)=2^x?

Answer 1

The correct answer for the exercise shown in the figure attached is first option, which is:

Shifted 4 units left, reflect over the x-axis, shift 2 units down

The explanation is shown below:

When you graph both function, the parent function and the transformated function, you can see clearly that the transformation is obtained by shifting it 4 units left and 2 units down.

Answer 2

Compairing g(x) with f(x), we can write:

To get g(x) f(x) is:
1) Multiplied by -1.
This implies the f(x) is reflected over x-axis

2) Addition of 4 to x
This implies f(x) is shifted 4 units to left

3) Subtraction of 2 to function value.
This implies f(x) is shifted down by 2 units.

So, we can write g(x) as:

g(x) = -f(x+4) - 2

So, the correct answer to this question is option A.
Shift 4 units left, reflect over x axis and shift 2 units down