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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.

User Kevindra
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1 Answer

21 votes
21 votes

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).

User Jonas Wolff
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