Functions can be transformed through translation, dilation, etc.
The function g(x) is [tex]g(x) = (x + 3)^2 - 1[/tex]
The question is incomplete, as the graph or the equation of f(x) are not given. So, I will use an assumed function.
Assume that the function f(x) is:
[tex]f(x) = x^2[/tex]
The transformation from f(x) to g(x) is as follows:
First, calculate f(x + 3)
[tex]f(x + 3) = (x + 3)^2[/tex]
Subtract 1 from both sides
[tex]f(x + 3) - 1 = (x + 3)^2 - 1[/tex]
We have:
[tex]g(x) = f(x + 3)-1[/tex]
Hence:
[tex]g(x) = (x + 3)^2 - 1[/tex]
Hence, the function g(x) is [tex]g(x) = (x + 3)^2 - 1[/tex]
Read more about function transformation at:
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