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If the ordered pair (2,4) is on the graph f(x), find one ordered pair that will be on the following functions:

Af(x)-3 b) f(x-3) c) 2 f(x) d) f(x-2)+1 e) -f(x)

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\((2,4) \hbox{ is on the graph of } f(x) \\ \Downarrow \\ f(2)=4\)

a)
\(f(x)-3 \\ \\ f(2)=4 \\ f(2)-3=4-3 \\ f(2)-3=1 \\ \Downarrow \\ f(x)-3=1 \hbox{ for } x=2 \\ \\ \hbox{an ordered pair: } \boxed{(2,1)}\)

b)
\(f(x-3) \\ \\ f(2)=4 \\ f(5-3)=4 \\ \Downarrow \\ f(x-3)=4 \hbox{ for } x=5 \\ \\ \hbox{an ordered pair: } \boxed{(5,4)}\)

c)
\(2f(x) \\ \\ f(2)=4 \\ 2 \times f(2)=2 \times 4 \\ 2f(2)=8 \\ \Downarrow \\ 2f(x)=8 \hbox{ for } x=2 \\ \\ \hbox{an ordered pair: } \boxed{(2,8)}\)

d)
\(f(x-2)+1 \\ \\ f(2)=4 \\ f(4-2)=4 \\ f(4-2)+1=4+1 \\ f(4-2)+1=5 \\ \Downarrow \\ f(x-2)+1=5 \hbox{ for } x=4 \\ \\ \hbox{an ordered pair: } \boxed{(4,5)}\)

e)
\(-f(x) \\ \\ f(2)=4 \\ -1 \times f(2)=-1 \times 4 \\ -f(2)=-4 \\ \Downarrow \\ -f(x)=-4 \hbox{ for } x=2 \\ \\ \hbox{an ordered pair: } \boxed{(2,-4)}\)

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