Question

Given the function f(x)=g(x-3)+2, describe transformation of f(x) on a coordinate plane relative to g(x).

Answer 1

The transformation of f(x) on a coordinate plane relative to g(x) is that the graph of g(x) has been shifted three units to the right and two units upward.

Explanation:

`If \ c \ is \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=g(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ f(x)=g(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ f(x)=g(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ f(x)=g(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ f(x)=g(x+c)`

By knowing this, we can see that the function
`f(x)` takes the following form:

`f(x)=g(x-c)+k`

Therefore, we can say that
`g(x-3)` represents shifting the graph three units to the right and ultimately
`g(x-3)+2` tells us that the graph is shifted two units upward. Finally:

• The transformation of f(x) on a coordinate plane relative to g(x) is that the graph of g(x) has been shifted three units to the right and two units upward.