We can see from the question that we have a case of the transformation of the absolute value:
Then this function can be represented as:
This is the parent function.
Therefore, to obtain the transformed function from this parent function, we can proceed as follows:
1. We can translate 4 units to the right the parent function:
[tex]y=|x-4|[/tex]
And we obtain:
2. Now, we can reflect the resulting function across the x-axis:
[tex]y=-|x-4|[/tex]
And we will get:
3. Finally, we need to translate the function 1 unit downward as follows:
[tex]y=-|x-4|-1[/tex]
And we have:
Which is the graph of the function in the question.
Therefore, in summary, the equation for the graph is:
[tex]y=-\lvert x-4\rvert-1[/tex]
[Option b]
