Question

The function f(x) = x was transformed to create a graph g(x) = f(x- 1) – 2.

Which statement describes how the graphs of fand g are related?

The graph of f is shifted to the left 1 unit and down 2 units to create the graph of g.

The graph of fis shifted to the right 1 unit and down 2 units to create the graph of g.

The graph of fis shifted to the right 1 unit and up 2 units to create the graph of g.

The graph of fis shifted to the left 1 unit and up 2 units to create the graph of g.

Answer 1

To get the graph of g(x) = f(x-1) -2, you'd shift the graph of f right 1 unit and down 2 units.

The "x-1" in f(x-1) is a horizontal shift (left/right) and those are the opposite of what you'd think. Subtraction moves right, addition moves left.

The "-2" at the end is a vertical shift and that is what you'd expect with subtraction moving you down.

Go with the second answer:

The graph of f is shifted to the right 1 unit and down 2 units to create the graph of g.

Answer 2

The correct statement that describes how the graphs of f and g are related is: `The graph of f is shifted to the right 1 unit and down 2 units to create the graph of g.`

The answer is option ⇒2

Step-by-step explanation:

To understand why this is the correct statement, let's analyze the transformation that occurred to the function f(x) = x to create g(x) = f(x-1) - 2.

1. The term (x-1) inside the function represents a horizontal shift to the right by 1 unit. This means that every point on the graph of f(x) is moved 1 unit to the right to create the graph of g(x).

2. The subtraction of 2 at the end of the function represents a vertical shift downwards by 2 units. This means that every point on the graph of f(x) is moved 2 units downwards to create the graph of g(x).

Therefore, combining both transformations, the graph of f is shifted to the right 1 unit and down 2 units to create the graph of g.

It's important to note that the transformation does not involve an upward shift, as stated in the other options. Understanding the effect of the transformations on the graph helps us accurately describe the relationship between f and g.

The answer is option ⇒2