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

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)`

Answer 2

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