Question

The graph of f(x) = x2 is shifted 3 units to the left to obtain the graph of g(x). Which of the following equations best describes g(x)?

Answer 1

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

Answer 2

we have

$f(x)=x^{2}$

This is the equation of a vertical parabola open upward with the vertex at point $(0,0)$

we know that

The graph of f(x) is is shifted $3$ units to the left to obtain the graph of g(x)

so

The rule of the translation is

$(x,y)------> (x-3,y)$

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

$(0,0)------> (0-3,0)$

$(0,0)------> (-3,0)$

The vertex of the graph of g(x) is the point $(-3,0)$

therefore

the answer is

The equation of g(x) is equal to

$g(x)=(x+3)^{2}$