Answer:
The required function is \(g\left(x\right)=\left(x+1\right)^2-2\).
Step-by-step 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 \(g\left(x\right)=\left(x+1\right)^2-2\).
