Question

The Graph Of The Function F(X) Is Shown On The Grid Below. The Function G Is Defined By The Formula G(X) = F(X+3)-1. graph and label g on the axes along with f

Answer 1

Functions can be transformed through translation, dilation, etc.

The function g(x) is $g(x) = (x + 3)^2 - 1$

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:

$f(x) = x^2$

The transformation from f(x) to g(x) is as follows:

First, calculate f(x + 3)

$f(x + 3) = (x + 3)^2$

Subtract 1 from both sides

$f(x + 3) - 1 = (x + 3)^2 - 1$

We have:

$g(x) = f(x + 3)-1$

Hence:

$g(x) = (x + 3)^2 - 1$

Hence, the function g(x) is $g(x) = (x + 3)^2 - 1$

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