What is the equation of the new function???

We know that the transformation which shifts a function along the horizontal x axis is given by [tex]f(x+a)[/tex], while its [tex]f(x-a)[/tex] 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:

[tex] g ( x ) = | x - 4 | + 6 [/tex]

Answer Link

luisejr77 luisejr77 · Answer 2 · 2019-07-07T19:29:39+02:00

Answer: Option C

[tex]g (x) = | x-4 | +6[/tex]

Step-by-step explanation:

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

[tex]g (x) = f (x + h)[/tex]

So:

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

If [tex]h <0[/tex] 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

[tex]g (x) = f(x) + k[/tex]

So

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

If [tex]k <0[/tex] 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 [tex]f(x) = | x |[/tex] and moves 4 units to the right and 6 units to the top, then the transformation is:

[tex]g (x) = f (x-4) +6[/tex]

[tex]g (x) = | x-4 | +6[/tex]