Answer:
The required function is [tex]g\left(x\right)=\left(x+1\right)^2-2[/tex].
Step-by-step explanation:
The given function is
[tex]f(x)=x^2[/tex]
The general equation is
[tex]g(x)=f(x+a)+b[/tex]
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.
[tex]g(x)=f(x+1)+(-2)[/tex]
[tex]g(x)=(x+1)^2-2[/tex] [tex][\because f(x)=x^2][/tex]
Therefore the required function is [tex]g\left(x\right)=\left(x+1\right)^2-2[/tex].
