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

What do I do here? I have to write the function’s equation but how?-example-1

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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

What do I do here? I have to write the function’s equation but how?-example-1
User Christiano
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