Question

G (x ), represents transformations on the parent function of y = (½) x Write the equation for g (x ).

Answer 1

Complete Question:

g(x), represents transformations on the parent function of
`y = ((1)/(2))^x`.

Write the equation for g (x ) with the following transformations:

Reflect over y-axis, and shift right 7

Answer:

`g(x) = ((1)/(2))^(-x-7)`

Explanation:

Given

`y = ((1)/(2))^x`

Represent the function as:

`f(x) = ((1)/(2))^x`

Taking the transformations, one after the other:

Reflect over the y-axis.

This is represented by the rule: (x,y) ==> (-x,y)

So, we have:

`f'(x) = ((1)/(2))^(-x)`

Shift right 7 units

This is represented by (x,y) = (x - b, y)

Where b represents the number of units

So, we have:

`f'(x-7) = ((1)/(2))^(-x-7)`

Hence:

`g(x) = ((1)/(2))^(-x-7)`