Given f(x)=3^x-2 and g(x)=f(3x)+4, write the function rule for function g and describe the types of transformations that occur between function f and function g.

The transformation that occurs from is compression by 3 units horizontally and shift  of 4 units upwards.

Step-by-step explanation:

Given

Translation Rules:

If the function is compressed units horizontally.

If and  the function stretches units horizontally.

If the function shifts units to the up.

If the function shifts units to the down.

Applying the rules to

Step 1

[compressed units horizontally]

Step 2

∴

[shifts 4 nits up]

∴ The transformation that occurs from is compression by 3 units horizontally and shift  of 4 units upwards.