Translation of a function
Let's image any function f(x):
We have that the function g(x) is the same f(x) but translated:
Let's analyze the ways of translate a function, by observing the relation between f(x) and g(x) in the given equation:
g(x) = f(x - 1) - 5
Horizontal shift
If we want to translate the function horizontally we add the number of unities to the x:
- if the number is positive it will be translated to the left.
- if the number is negative it will be translated to the right.
In this equation the x has added -1:
f(x - 1) - 5 ⇒ x - 1
since -1 is negative then the function is translated one unity to the right:
Vertical shift
If we want to translate the function vertically we add the number of unities outside the equation:
- if the number is positive it will be translated upwards.
- if the number is negative it will be translated downwards.
In the equation, there is added -5 to the whole equation f(x - 1):
f(x - 1) - 5 ⇒ - 5
since -5 is negative, then the function is translated five unities downwards:
Summary
Then, the function is translated one unity to the right and five unities downwards
Answer: C
