Answer:
[tex]g(x)=x+4[/tex]
Step-by-step explanation:
Given
[tex]f(x)=x[/tex]
[tex]g(x)\rightarrow f(x)[/tex] shifted 7 units left and 3 units down
Translation Rules:
[tex]f(x)\rightarrow f(x+c)[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the left.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the right.
[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]
[tex]f(x)\rightarrow f(x+7)[/tex] [7 units left]
[tex]f(x+7)\rightarrow f(x+7)-3[/tex] [3 units down]
∴ [tex]g(x)=f(x+7)-3=(x+7)-3=x+7-3=x+4[/tex]
[tex]g(x)=x+4[/tex]
