Explanation:
Concept:
How do you translate an equation to the right?
To shift, move, or translate horizontally, replace y = f(x) with y = f(x + c) (left by c) or y = f(x - c) (right by c).
To translate an equation down, we will use the formula below
[tex]\begin{gathered} y=f(x)-k \\ \end{gathered}[/tex]
The parent functionof the graph on the question is given below as
[tex]f(x)=x^2[/tex]
From the graph, we can see that the graph was translated horizontally to the left by 1 units and with this , we will have the equation become
[tex]\begin{gathered} y=f(x+1) \\ y=(x+1)^2 \end{gathered}[/tex]
We can also see that the tranlated graph was shifted vertically by 1 units
Hence,
We will have the new equation to be
[tex]\begin{gathered} y=f(x)-1 \\ y=(x+1)^2-1 \end{gathered}[/tex]
Hence,
The final answer is
[tex]f(x)=(x+1)^2-1[/tex]
THE FIRST OPTION IS THE CORRECT ANSWER
