Question

I would like to know how to format a function equation after it has been translated

Answer 1

EXPLANATION :

From the problem, we can see that the graph of g is to the right and below the graph of f.

We need to choose a specific point that is common between the two graphs.

For function f, we can choose the vertex (0, 0).

And in function g, the vertex is (3, -4)

We can compare the vertices :

The x-coordinate was translated from 0 to 3, so it moves 3 units to the right.

The y-coordinate was translated from 0 to -4, so it moves 4 units downward.

The translated function will be in the form :

`g(x)=f(x-c)-d`

where c = number of units shifted to the right

d = number of units shifted downward.

So we have c = 3 and d = 4

The function will be :

`g(x)=f(x-3)-4`

Note that f(x) is :

`\begin{gathered} f(x)=x^2 \\ \text{ Then : }f(x-3)\text{ will be :} \\ \\ f(x-3)=(x-3)^2 \end{gathered}`

Then g(x) will be :

`g(x)=(x-3)^2-4`

ANSWER :

g(x) = (x - 3)^2 - 4