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.