Question

If g(x) = 3x + 12, which statement is true?

A.
The rate of change of g(x) is less than the rate of change of f(x).

B.
The x-intercept of g(x) is less than the x-intercept of f(x).

C.
The rate of change of g(x) is greater than the rate of change of f(x).

D.
The x-intercept of g(x) is greater than the x-intercept of f(x).

Answer 1

The rate of change of g(x) is 3, which is greater than the rate of change of f(x), which is 2. Option C is the right choice.

Here is my analysis of the statements:

Statement A: The rate of change of g(x) is 3, which is greater than the rate of change of f(x), which is 2. Thus, statement A is false.

Statement B: The x-intercept of g(x) is -4, which is less than the x-intercept of f(x), which is -5. Thus, statement B is false.

Statement C: The rate of change of g(x) is 3, which is greater than the rate of change of f(x), which is 2. Thus, statement C is true.

Statement D: The x-intercept of g(x) is -4, which is less than the x-intercept of f(x), which is -5. Thus, statement D is false.

Therefore, the only true statement is option C. The rate of change of g(x) is greater than the rate of change of f(x).