Question

Compare two functions involving a negative factor.

pH = -log x and y = Poe-2
Choose all statements that are correct.
A. Both the logarithmic function and the exponential function represent change that is not linear.
B. The logarithmic function can have no negative x-values; the exponential function can have no negative y-values.
C. The base of the logarithmic function and the base of the exponential function are both positive.
D. The output of the logarithmic function can only be negative, but the output of the exponential function can only be positive.

Answer 1

Okay, let's evaluate the statements:

A. This is correct. Both logarithmic and exponential functions represent non-linear change.

B. This is incorrect. The logarithmic function can have negative x-values and the exponential function can have negative y-values.

C. This is correct. The base of the logarithm (which is -1 here) and the base of the exponential (which is e here, approximately 2.718) are positive.

D. This is incorrect. The logarithmic function can produce negative or positive output depending on the input x. The exponential function can also produce negative or positive output depending on the input.

So the correct statements are:

A. Both the logarithmic function and the exponential function represent change that is not linear.

C. The base of the logarithmic function and the base of the exponential function are both positive.

In summary, I would choose options A and C.

Let me know if you have any other questions!