F(x) = 0.2^x is transformed 9 units right, compressed vertically by a factor of 1/6 and reflected across the x-axis. write the transformed function g(x)

g(x) = -⅙(0.2)^(x – 9)

Step-by-step explanation:

F(x) = 0.2^x

(a) Transformation to the right

You transform a function 9 units to the right by subtracting 9 from the value of x. Thus, the function becomes

F₁(x) = 0.2^(x – 9)

(b) Vertical compression

To compress a function vertically by a factor of 6, you divide the whole function by 6. Thus, the function becomes

F₂(x) = ⅙F₁(x) =  ⅙(0.2)^(x – 9)

(c) Reflection across x-axis

When you reflect a point (x, y) across the x-axis, the x-coordinate remains the same, but the y-coordinate gets the opposite sign. Thus,

g(x) =  -⅙(0.2)^(x – 9)

The image below shows F(x) and its appearance after each of the operations.