Question

Which is the transformation rule and the function rule for g(x).

Select two answers: one for the transformation rule and one for the function rule

a. g(x) = log₅(x + 2) + 4
b. g(x) = f(x- 3) - 2
c. g(x) = log₅(x - 2) + 4
d. g(x) = f(x - 2) + 3
e. g(x) = log₅(x - 2) - 4
f. g(x) = f(x + 2) + 3

Answer 1

The transformation rule is g(x) = log₅(x - 2) + 4, indicating a horizontal and vertical shift, while the function rule is represented by g(x) = f(x - 2) + 3, defining the shifts applied to an unspecified function f(x).

Step-by-step explanation:

To determine the transformation rule and the function rule for g(x), we must look at the structure of the given functions. A transformation rule describes how a function is shifted, stretched, or reflected, while the function rule specifies the general form or type of the function.

Of the provided options:

• The function g(x) = log₅(x - 2) + 4 shows a logarithmic function with a base of 5. The transformation rule here is a horizontal shift to the right by 2 units and a vertical shift up by 4 units.
• The function g(x) = f(x - 2) + 3 implies that g(x) is another function, f(x), that has been horizontally shifted to the right by 2 units and vertically shifted up by 3 units. It doesn't specify the type of function f(x) is, but it indicates the transformation applied to it.

Therefore, the transformation rule is g(x) = log₅(x - 2) + 4 for a logarithmic function and the function rule can be seen in g(x) = f(x - 2) + 3 as it applies a transformation to f(x) without changing its general form.