Question

What do I do here? I have to write the function’s equation but how?

Answer 1

Step-by-step 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

`\begin{gathered} y=f(x)-k \\ \end{gathered}`

The parent functionof the graph on the question is given below as

`f(x)=x^2`

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

`\begin{gathered} y=f(x+1) \\ y=(x+1)^2 \end{gathered}`

We can also see that the tranlated graph was shifted vertically by 1 units

Hence,

We will have the new equation to be

`\begin{gathered} y=f(x)-1 \\ y=(x+1)^2-1 \end{gathered}`

Hence,

The final answer is

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

THE FIRST OPTION IS THE CORRECT ANSWER