Question

f(x)=4^x and g(x)=4^x+2

State the type of transformation from f(x) to g(x) in the problem above and including its distance moved.

Answer 1

Given:

The two functions are:

$f(x)=4^x$

$g(x)=4^x+2$

To find:

The type of transformation from f(x) to g(x) in the problem above and including its distance moved.

Solution:

The transformation is defined as

$g(x)=f(x+a)+b$                .... (i)

Where, a is horizontal shift and b is vertical shift.  

• If a>0, then the graph shifts a units left.
• If a<0, then the graph shifts a units right.
• If b>0, then the graph shifts b units up.
• If b<0, then the graph shifts b units down.

We have,

$f(x)=4^x$

$g(x)=4^x+2$

The function g(x) can be written as

$g(x)=f(x)+2$            ...(ii)

On comparing (i) and (ii), we get

$a=0,b=2$

Therefore, the type of transformation is translation and the graph of f(x) shifts 2 units up to get the graph of g(x).