The function given is:

$f(x) = 2^x$

Horizontal Shift Rule

To shift a function h units to the right, we replace $x$ with $(x - h)$:

$g(x) = f(x - h)$

Since the graph is shifted right by 6 units, we set $h = 6$, so:

$g(x) = 2^{(x - 6)}$

Thus, the equation of the new function is:

$g(x) = 2^{x - 6}$

Would you like a step-by-step explanation of why shifting right involves subtracting from $x$?

Related Questions

1. What would be the equation if the graph was shifted left by 4 units instead?
2. How does shifting up or down affect the equation of the function?
3. How do we reflect $f(x) = 2^x$ across the x-axis?
4. What happens to the asymptote of $f(x)$ after shifting right by 6 units?
5. How would the equation change if we wanted to shift the function diagonally (both right and up)?

Math Tip

When shifting horizontally, always remember:

• Right shift → replace $x$ with $x - h$.
• Left shift → replace $x$ with $x + h$.
  This applies to all function types, including exponentials, quadratics, and trigonometric functions.