Question

Which function represents a horizontal shift of f(x)=5^x by 4 units to the right?

Answer 1

If you have a function y = f(x), the transformation along the x-axis is given by:

y = f(x+a) ⇒ This is the translation to the LEFT by 'a' units
y = f(x-a) ⇒ This is the translation to the RIGHT by 'a' units

So you have, f(x) = 5ˣ, translated 4 unit right will give g(x) = 5⁽ˣ⁻⁴⁾

Answer 2

Answer: $g(x)=5^{x-4}$

Step-by-step explanation:

When a function f(x) is shifted horizontally by n units to the right , the new function will become :-

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

The given function : $f(x)=5^x$

Now, if the given function shifted 4 units to the right , then the new function will become :

$g(x)=f(x-4)$

$g(x)=5^{x-4}$

Hence, the  function represents a horizontal shift of $f(x)=5^x$ by 4 units to the right will be :-

$g(x)=5^{x-4}$