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 $y = (\frac{1}{2})^x$.

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

Reflect over y-axis, and shift right 7

Answer:

$g(x) = (\frac{1}{2})^{-x-7}$

Step-by-step explanation:

Given

$y = (\frac{1}{2})^x$

Represent the function as:

$f(x) = (\frac{1}{2})^x$

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:

$f'(x) = (\frac{1}{2})^{-x}$

Shift right 7 units

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

Where b represents the number of units

So, we have:

$f'(x-7) = (\frac{1}{2})^{-x-7}$

Hence:

$g(x) = (\frac{1}{2})^{-x-7}$