Question

What is the equation of the new function???

Answer 1

Answer: Option C

`g (x) = | x-4 | +6`

Explanation:

If we have a main function and perform a transformation of the form

`g (x) = f (x + h)`

So:

If
`h> 0` the graph of the function g(x) will be equal to the graph of f(x) displaced h units to the left

If
`h <0` the graph of the function g(x) will be equal to the graph of f(x) displaced h units to the right

Also if the transformation is done

`g (x) = f(x) + k`

So

If
`k> 0` the graph of the function g(x) will be equal to the graph of f(x) displaced k units up

If
`k <0` the graph of the function g(x) will be equal to the graph of f(x) displaced k units downwards.

In this case the main function is
`f(x) = | x |` and moves 4 units to the right and 6 units to the top, then the transformation is:

`g (x) = f (x-4) +6`

`g (x) = | x-4 | +6`

Answer 2

The correct answer option is C.
`g ( x ) = | x - 4 | + 6`.

Explanation:

We know that the transformation which shifts a function along the horizontal x axis is given by
`f(x+a)`, while its
`f(x-a)` which shifts the function to the right side.

Here we are to shift the function 4 units to the right and 6 units up.

Therefore, the function will be:

`g ( x ) = | x - 4 | + 6`