Transformation of f(x)=x²−1 to g(x)=(x+4)²−1 is a horizontal translation 4 units to the left.
Given function is
[tex]f(x) = x^{2} -1[/tex]
How horizontal translation of a graph takes place?
A function f(x) becomes f(x+k) when it is translated horizontally by k units (k greater than zero) in the left direction or direction of negative x. Similarly, f(x) becomes f(x-k) when it is translated horizontally by k units in the right direction.
Translated [tex]f(x) =(x+4)^2-1[/tex]
Here, x is being replaced by x+4, This means f(x) is translated horizontally by 4 units to the left.
Therefore, transformation of f(x)=x²−1 to g(x)=(x+4)²−1 is a horizontal translation 4 units to the left.
To get more about graph translation visit:
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