Question

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

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

Answer 1

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