Answer:
Shift [tex]f(x)=6^x[/tex] 5 units to the right and 7 units down.
Option B is correct.
Step-by-step explanation:
Given: [tex]f(x)=6^x[/tex] translate to [tex]g(x)=6^{x-5}-7[/tex]
Using translation property
If [tex]x\rightarrow x+a[/tex] then function shift horizontally.
If a>0 then shift left
If a<0 then shift right
If [tex]f(x)\rightarrow f(x)+a[/tex] then function shift vertically.
If a>0 then shift up
If a<0 then shift down
[tex] f(x)=6^x [/tex]
[tex] g(x)=6^{x-5}[/tex]
f(x) shift 5 unit right.
[tex] g(x)=6^{x-5}-7[/tex]
f(x) shift 7 unit down.
Hence, {tex]f(x)=6^{x}[/tex] translate to [tex]g(x)=6^{x-5}-7[/tex]
Shift [tex]f(x)=6^x[/tex] 5 units to the right and 7 units down.
