Answer:
[tex]\large\boxed{21.\ g(x)=f(x-2)+1\to g(x)=\log_3(x-2)+1}\\\\\boxed{22.\ g(x)=f(x)-4\to g(x)=3^x-4}\\\\\boxed{23.\ g(x)=-f(x)\to g(x)=-\log_{\frac{1}{2}}x}[/tex]
Step-by-step explanation:
f(x) + n - shift the grapf n units up
f(x) - n - shift the grapf n units down
f(x + n) - shift the grapf n units to the left
f(x - n) - shift the grapf n units to the right
-f(x) - reflection about the x-axis
f(-x) - reflection about the y-axis
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Look at the picture.
[tex]21.\\f(x)=\log_3x\\\\g(x)=\log_3(x-2)+1[/tex]
move the graph 2 units to the right and 1 unit up
[tex]22.\\f(x)=3^x\\\\g(x)=3^x-4[/tex]
move the graph 4 units down
[tex]23.\\f(x)=\log_{\frac{1}{2}}x\\\\g(x)=-\log_{\frac{1}{2}}x[/tex]
reflection the graph about the X axis.
