Question

Using the graph of f(x)=x^2 as a guide describe the transformations and then sketch a graph of each function g(x)=(x+1)^2+3

Answer 1

According to the Transformation rules for functions:

1) When a function f(x) is shifted left "k" units:

`f\mleft(x+k\mright)\text{ }`

2) When it is shifted right "k" units:

`f\mleft(x-k\mright)`

3) When it is shifted up "k" units:

`f(x)+k`

4) When it is shifted down "k" units:

`f(x)-k`

Observe in the graph attached that the vertex of the following parent function is located at the origin:

`f(x)=x^2`

Knowing that the function g(x) is:

`g\mleft(x\mright)=\mleft(x+1\mright)^2+3`

You can determine that the function g(x) is the function f(x) but shifted left 1 unit and shifted up 3 units.