Question

F(x) = x2 + 3x + 2 is shifted 2 units left. The result is g(x). What is g(x)?

Answer 1

`g(x) = x^2+7x+12`

Explanation:

If we are given a function f and we want to shift it a units horizontally, the resulting function will be f(x - a), where a positive a is a shift rightwards and a negative a is a shift leftwards.

We have the function:

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

And we want to shift it two units to the left.

Since we want to shift it two units to the left, a = -2. Therefore, our new function, let's call it g, must be f(x - (-2)) or f(x + 2). Substitute:

`g(x) = f(x+2)=(x+2)^2+3(x+2)+2`

Simplify. Expand:

`g(x) = (x^2+4x+4)+(3x+6)+2`

Combine like terms. Hence:

`g(x) = x^2+7x+12`