Question

The graph of f, of, x, equals, 2, to the power xf(x)=2
x
is given below. Write the equation of a function g, of, xg(x) which would shift the graph of f, of, xf(x) right 6 units.

Answer 1

To shift the graph of the function \( f(x) = 2^x \) to the right by 6 units, you need to replace \( x \) with \( x - 6 \) in the function's formula. This transformation is what causes the horizontal shift to the right.

Thus, the equation for the new function \( g(x) \) would be:

\[
g(x) = f(x - 6) = 2^{(x - 6)}
\]

This can also be written as:

\[
g(x) = 2^x \cdot 2^{-6} = \frac{2^x}{64}
\]

However, the most straightforward form, indicating the shift, is:

\[
g(x) = 2^{(x - 6)}
\]

So the final answer is:

\[
g(x) = 2^{(x - 6)}
\]