[tex](2,4) \hbox{ is on the graph of } f(x) \\ \Downarrow \\ f(2)=4[/tex]
a)
[tex]f(x)-3 \\ \\ f(2)=4 \\
f(2)-3=4-3 \\
f(2)-3=1 \\ \Downarrow \\
f(x)-3=1 \hbox{ for } x=2 \\ \\
\hbox{an ordered pair: } \boxed{(2,1)}[/tex]
b)
[tex]f(x-3) \\ \\ f(2)=4 \\
f(5-3)=4 \\ \Downarrow \\
f(x-3)=4 \hbox{ for } x=5 \\ \\
\hbox{an ordered pair: } \boxed{(5,4)}[/tex]
c)
[tex]2f(x) \\ \\
f(2)=4 \\
2 \times f(2)=2 \times 4 \\
2f(2)=8 \\ \Downarrow \\ 2f(x)=8 \hbox{ for } x=2 \\ \\
\hbox{an ordered pair: } \boxed{(2,8)}[/tex]
d)
[tex]f(x-2)+1 \\ \\
f(2)=4 \\
f(4-2)=4 \\
f(4-2)+1=4+1 \\
f(4-2)+1=5 \\ \Downarrow \\
f(x-2)+1=5 \hbox{ for } x=4 \\ \\
\hbox{an ordered pair: } \boxed{(4,5)}[/tex]
e)
[tex]-f(x) \\ \\
f(2)=4 \\
-1 \times f(2)=-1 \times 4 \\
-f(2)=-4 \\ \Downarrow \\
-f(x)=-4 \hbox{ for } x=2 \\ \\
\hbox{an ordered pair: } \boxed{(2,-4)}[/tex]
