Question

If you shift the exponential parent function, f(x) = 2^x , right 2 units, what is the equation of the new function?

Answer 1

We know the rule for shifting right(x is changed)

• f(x) —» f(x-a)

So

here

For a =2

• f(x-2)
• 
  `\sf 2^(x-2)`

Answer 2

`g(x)=2^(x-2)`

Explanation:

Translations

For
`a > 0`

`f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}`

`f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}`

Parent function:
`f(x)=2^x`

Translated 2 units right:
`g(x)=f(x-2)=2^(x-2)`