Question

Suppose g(x) = f(x - 1) - 5. Which statement best compares the graph ofg(x) with the graph of f(x)?A. The graph of g(x) is shifted 1 unit left and 5 units up.B. The graph of g(x) is shifted 1 unit left and 5 units down.OOOOC. The graph of g(x) is shifted 1 unit right and 5 units down.D. The graph of g(x) is shifted 1 unit right and 5 units up.

Answer 1

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