Logarithm properties:

According to this, we can get:
Given:
The graph of a function.
To find:
The range of the given function using interval notation.
Solution:
Range: The set of y-values or output values are known as range.
From the given graph, it is clear that the function is defined for
and the values of the functions lie between -2 and 2, where -2 is excluded and 2 is included.
Range 
The interval notation is:
Range ![=(-2,2]](https://tex.z-dn.net/?f=%3D%28-2%2C2%5D)
Therefore, the range of the given function is (-2,2].
While the vertex of the function f(x) = x^2 is (0, 0), the vertex of the function g(x) = x^2 + 2x + 1 is (-1, 0).
Whereas both function has same y-cordinate, their x-coordinate are different which indicates that the function g(x) = x^2 + 2x + 1 is a horizontal translation of the function f(x) = x^2.