Question

The function f(x) = x was transformed to form g(x) = f(x) - 23.

Which statement is true about the graphs of f and g?

A. The graphs of f and g are not parallel, and the graph of f is translated 23 units up to create the graph of g.
B. The graphs of f and g are not parallel, and the graph of f is translated 23 units down to create the graph of g.
C. The graphs of f and g are parallel, and the graph of fis translated 23 units up to create the graph of g.
D. The graphs of fand g are parallel, and the graph of f is translated 23 units down to create the graph of g.

Answer 1

It’s either A, B, C, or D, I have no clue which though, good luck

Answer 2

The correct statement regarding the graphs is D: The graphs of f(x) = x and g(x) = f(x) - 23 are parallel, and the graph of f is translated 23 units down to create the graph of g.

Step-by-step explanation:

To determine the relationship between the graphs of the functions f(x) = x and g(x) = f(x) - 23, it is important to understand the effect of subtracting a number from a function. In this case, subtracting 23 from f(x) means that every y-value on the graph of f(x) is reduced by 23 units. This transformation results in a vertical translation (or shift) of the original graph downwards by 23 units. Therefore, the graphs of f and g will be parallel, and the graph of f is moved 23 units downwards to create the graph of g. Hence, the correct statement is D: The graphs of f and g are parallel, and the graph of f is translated 23 units down to create the graph of g.