Question

Which best describes the range of the function f(x) = 2/3(6)x after it has been reflected over the x-axis?

Answer 1

Your post (" f(x) = 2/3(6)x ") would be clearer and less ambiguous if you'd please format it as follows:

f(x) = (2/3)(6)^x.  The (2/3) shows that 2/3 is the coefficient of the exponential function 6^x.  Please use " ^ " to indicate exponentiation.

Start by graphing   f(x) = (2/3)(6)^x.  The y-intercept, obtained by setting x=0, is (0, 2/3).  Can you show that the value of f(x) is (2/3)*6, or 4, at x=1, (2/3)*6^2, or 24, at x = 2, and so on?  What happens if x becomes increasingly smaller?  The graph approaches, but does not touch, the x-axis.

If you complete this graphing assignment, then all you'd have to do is to flip the whole graph over vertically, reflecting it in the x-axis.  You'll see that the graph never touchs the x-axis.  Therefore, the range of this flipped graph is (-infinity, 0).

Answer 2

Answer:

The correct answer is:

D) all real numbers less than or equal to 0.

Step-by-step explanation: