Question

Which of the ten basic functions in

our toolkit are decreasing on the
interval (-0, 0)?
A. x2, 1, X
B. ex, x2, In(x)
C. x3, xl,
D. Vx, x3, x2

Answer 1

The decreasing functions on the interval (-0, 0) are: ex, x², ln(x).

Step-by-step explanation:

The decreasing functions on the interval (-0, 0) are:

1. x²
2. ex
3. ln(x)

Let's go through each option and determine whether the given functions are decreasing on the interval (-0, 0):

1. Option A: x² is not decreasing on the interval (-0, 0) because it becomes more positive as x approaches 0 from the negative side.
2. Option B: The function ex is decreasing on the interval (-0, 0) because as x approaches 0 from the negative side, the function approaches 1/e, which is less than 1. The function x² is not decreasing on the interval (-0, 0) for the same reason as in Option A. The function ln(x) is not defined for negative values of x, so it is not applicable.
3. Option C: x³ is not decreasing on the interval (-0, 0) because it becomes more negative as x approaches 0 from the negative side. The function x is not defined for negative values of x, so it is not applicable.
4. Option D: The function √x is not decreasing on the interval (-0, 0) because it becomes more positive as x approaches 0 from the negative side. The functions x³ and x² are not defined for negative values of x, so they are not applicable.

Therefore, the correct answer is Option B: ex, x², ln(x) as these functions are decreasing on the interval (-0, 0).