Answer :
Answer:
[tex]g(x)=3^{3x}+2[/tex]
The transformation that occurs from [tex]f(x)\rightarrow g(x)[/tex] is compression by 3 units horizontally and shift of 4 units upwards.
Step-by-step explanation:
Given
[tex]f(x)=3^x-2[/tex]
[tex]g(x)=f(3x)+4[/tex]
Translation Rules:
[tex]f(x)\rightarrow f(cx)[/tex]
If [tex]c>1[/tex] the function is compressed [tex]c[/tex] units horizontally.
If [tex]c<1[/tex] and [tex]c>0[/tex] the function stretches [tex]c[/tex] units horizontally.
[tex]f(x)\rightarrow f(x)+c[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the up.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the down.
Applying the rules to [tex]f(x)[/tex]
Step 1
[tex]f(x)\rightarrow f(3x)[/tex]
[tex]f(3x)=3^{3x}-2[/tex]
[compressed [tex]3[/tex] units horizontally]
Step 2
[tex]f(3x)\rightarrow f(3x)+4=g(x)[/tex]
[tex]f(3x)+4=3^{3x}-2+4[/tex]
∴ [tex]g(x)=3^{3x}+2[/tex]
[shifts 4 nits up]
∴ The transformation that occurs from [tex]f(x)\rightarrow g(x)[/tex] is compression by 3 units horizontally and shift of 4 units upwards.