Question

The parent function of f(x)=3× is to be shifted 4 to the right and 3 up. What would the new equation be?

Answer 1

`g(x)=3(x-3)+3`

Explanation:

Translations

`\textsf{For}\quad a > 0`

`f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}`

`f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}`

Parent function:
`f(x)=3x`

Translated 4 units right:
`f(x-4)=3(x-4)`

Translated 3 units up:
`f(x-4)+3=3(x-4)+3`