Question

If f(x) = 44, which statements are true of g(x)?

A) g(4) = 1 and the graph is translated left 1 unit.
B) g(4) = 4 and the graph is translated down 1 unit.
C) The graph is translated both horizontally and vertically.
D) The domain and range of g(x) are the same as the domain and range of f(x).

Answer 1

The domain of f(x) is 0 to 20, and its range is the constant value of 44. Without specific information about g(x), we cannot ascertain translations or specific values like g(4). Assuming g(x) is a horizontal translation of f(x), the domain and range would be the same.

Step-by-step explanation:

If f(x) = 44, we know that the graph of f(x) is a horizontal line at y = 44. The domain is restricted to 0 ≤ x ≤ 20, meaning the function is defined only for x values within that interval. Thus, the domain consists of real numbers from 0 to 20, and the range is the constant value 44.

To determine which statements are true about g(x) based on this information, we need to recall some basic algebra principles:

• f(x - d) translates the function d units to the right.
• f(x + d) translates the function d units to the left.
• Adding or subtracting a constant from f(x) translates the function up or down, respectively.

Without specific information about g(x), we cannot determine points like g(4) or the specific translations applied to the function. We can note, however, that if g(x) were a translation of f(x), then it would have the same domain and range as long as the translation is horizontal. A vertical translation would change the range but not the domain. Without further details on g(x), Option D could be considered true, assuming g(x) is a horizontal translation of f(x) and no other transformations are applied.