Respuesta :

Edufirst
When you add a positive value to the argument of a function, its graph shifts to the left, the same number of units added to the argument.

This is, the graph of f(x+a) is the graph of the function f(x) shifted a units to the left.

Then, g(x) is f(x+3) = (x+3)^2
calculista

we have

[tex]f(x)=x^{2}[/tex]

This is the equation of a vertical parabola open upward with the vertex at point [tex](0,0)[/tex]

we know that

The graph of f(x) is is shifted [tex]3[/tex] units to the left to obtain the graph of g(x)

so

The rule of the translation is

[tex](x,y)------> (x-3,y)[/tex]

Applying the rule of the translation at the vertex of the graph of f(x)

[tex](0,0)------> (0-3,0)[/tex]

[tex](0,0)------> (-3,0)[/tex]

The vertex of the graph of g(x) is the point [tex](-3,0)[/tex]

therefore

the answer is

The equation of g(x) is equal to

[tex]g(x)=(x+3)^{2}[/tex]

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