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

Answer:

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

Step-by-step 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:  $g(x)=f(x-2)=2^{x-2}$

Answer 2

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

• f(x) —» f(x-a)

So

here

For a =2

• f(x-2)
• $\sf 2^{x-2}$