I need some help in my homework

[Igi2408]

1. The figure below shows the graph of the function f with domain (-4,5) and range(-3,3) .
Sketch the following transformation on the same grid, then determine the domain and range of the transformed function, g. Express your answers using interval notation. g(x)=f(x+2)-1

[Guest]

Can you upload a figure?

[Guest]

There is NO "figure below"!

Since f has domain "-4 to 5", x+ 2 can be as low as x+ 2= -4 so x can be as low as -6. x+ 2 can be a high as x+ 2= 5 so x can be as high as 3. g(x)= f(x+ 2) has domain -6 to 3. Since g(x)= f(x+2)- 1 and f has range -3 to 3, g has range -3-1= -4 to 3- 1= 2.

[GeradHum]

To graph g(x) = f(x + 2) - 1:

The +2 shifts the graph 2 units left.

The –1 shifts it 1 unit down.

So the domain becomes (–6, 3) and the range becomes (–4, 2).
Just shift the entire original graph accordingly!

[mycalsuite]

Domian (-6,3), Range: (-4,2)