Translations involve the movement of a function across the coordinates.
The equation of the red line is [tex]y + 3 = f(x)[/tex]
We have:
[tex]y =f(x)[/tex] --- the equation of the black line
From the graph, we can see that the black line is shifted down by 3 units, to create the red line.
The translation rule of downward movement is:
[tex]y = f(x) - h[/tex]
Where h is the number of units moved down
In this case:
[tex]h = 3[/tex]
So, we have:
[tex]y = f(x) -3[/tex]
Add 3 to both sides
[tex]y + 3 = f(x)[/tex]
Hence, the equation of the red line is [tex]y + 3 = f(x)[/tex]
Read more about translations at:
https://brainly.com/question/12463306
