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We have a graph and we need to make it look like a translated function that we have marked within the same graph.
The first thing we do is put a negative sign, this is to change the values of the function from the positive region on the y-axis to the negative region on the y-axis.
The second will be to move the function horizontally 5 units to the right, for this, we use the following rule:
y = f(x-c) where will move horizontally "c" units to the right.
Observing the image, we can see that we must move 5 units the function that is to say that in this case, we have f(x-5)
Finally, we must move the function vertically 1 unit down, for this, we use the following rule:
y = f(x)-1 y = f(x-c) where will move vertically "c" units downward.
Observing the image, we can see that we must move a unit the function that is to say that in this case, we have f(x)-1
In conclusion, the function that describes the way we should go about it is as follows:
[tex]y=-(x-5)^2-1[/tex]