If the function [tex]f(x) = x^2[/tex] is translated, the translated version of f(x) can be:
[tex]g(x) = (x+b)^2[/tex] (shifted b units to the left)
[tex]g(x) = (x-b)^2[/tex] (shifted b units to the right)
[tex]g(x) = x^2+b[/tex] (shifted b units upwards)
[tex]g(x) = x^2-b[/tex] (shifted b units downwards)
The given function is:
[tex]f(x) = x^2[/tex]
Translation can be done vertically and horizontally
For horizontal translation:
If the function f(x) is shifted b units to the left, the resulting function becomes:
[tex]g(x) = (x+b)^2[/tex]
If the function f(x) is shifted b units to the right, the resulting function becomes:
[tex]g(x) = (x-b)^2[/tex]
For vertical translation:
If the function f(x) is shifted b units upwards, the resulting function becomes:
[tex]g(x) = x^2+b[/tex]
If the function f(x) is shifted b units downwards, the resulting function becomes:
[tex]g(x) = x^2-b[/tex]
Learn more here: https://brainly.com/question/18758717
