Question

choose the function correctly identify the transformation of f(x)=x^2 shifted two units down and one unit to the left

Answer 1

(x+1)^2-1

...............

Answer 2

The required function is
`g\left(x\right)=\left(x+1\right)^2-2`.

Explanation:

The given function is

`f(x)=x^2`

The general equation is

`g(x)=f(x+a)+b`

Where, a represents the horizontal shift and b represents the vertical shift.

→ If a>0, then the graph of f(x) shifts left by a units and if a<0, then the graph of f(x) shifts right by a units.

→If b>0, then the graph of f(x) shifts upward by b units and if b<0, then the graph of f(x) shifts downward by b units.

Since the graph of f(x) shifted two units down and one unit to the left, therefore the value of b is -2 and the value of a is 1.

`g(x)=f(x+1)+(-2)`

`g(x)=(x+1)^2-2`
`[\because f(x)=x^2]`

Therefore the required function is
`g\left(x\right)=\left(x+1\right)^2-2`.