Question

Which equation for g(x) represents the transformation of f(x) given that f(x) = x^2

g(x) = f(x) shifted left 2 units?


PLEASE HELPPP

Answer 1

• Shifted left 2 units(Change in x y remains constant

Lets shift

`\\ \rm\Rrightarrow f(x)=x^2`

`\\ \rm\Rrightarrow g(x)=(x+2)^2`

`\\ \rm\Rrightarrow g(x)=x^2+2x+4`

Answer 2

g(x) = (x + 2)²

Explanation:

In function notation, if we want to shift a function to the left, we add the number we are asked to move to the left inside the function's argument:

⇒ To shift f(x) b units to left → f(x + b)

Similarly, if we want to shift a function to the right, we subtract the number we are asked to move to the right inside the function's argument:

⇒ To shift f(x) b units to right → f(x - b)

Given function f(x) = x²

Shift 2 units to the left: f(x + 2) = (x + 2)²

Therefore, g(x) = (x + 2)²