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.

Given:

The two functions are:

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

               .... (i)

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

We have,

The function g(x) can be written as

           ...(ii)

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

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

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

mark brainliest.