y = 2x - 1
Lets see something:
y = 2x - 1
y = f(x)
If we want to do translations in vertical we just have to add an constant, where postive moves it upward and negatives, downward
y = f(x) + c
y = f(x) - 1
y = 2x - 1 - 1
y = 2x - 2
Now let's see this translation to the right
If we want to translate it in horizontal we just have to add a constant inside the function, where positive moves it to the left, and negative to the right
y = f(x) - 1
y = f(x - 3) - 1
y = 2.(x - 3) - 1 - 1
y = 2x - 6 - 2
y = 2x - 8