When a function is translated, it means the function is moved away from its original position.
The function g(x) is: [tex]g(x) = (x + 5)^2 - 3[/tex]
Give that:
[tex]f(x) = x^2[/tex]
The rule of translation 5 units left is:
[tex](x,y) \to (x + 5, y)[/tex]
So, we have:
[tex]f'(x) = (x + 5)^2[/tex]
The rule of translation 3 units down is:
[tex](x,y) \to (x, y-5)[/tex]
So, we have:
[tex]g(x) = (x + 5)^2 - 3[/tex]
Hence, the function g(x) is: [tex]g(x) = (x + 5)^2 - 3[/tex]
Read more about translations at:
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