Which monomial function is described by the following statements?

as x > 0 increases, f(x) increases. as x < 0
decreases, f(x) decreases.

a. odd monomial function with negative a

b. odd monomial function with positive a

c. even monomial function with positive a

d. even monomial function with negative a

Option:b is the correct answer.

b. odd monomial function with positive a.

Step-by-step explanation:

Let us consider a monomial function as:

                                ⇒If a is negative.

Case 1:

if n is odd.

then As x>0 increases.

f(x) decreases.

and if x<0 decreases.

f(x) increases.

Case 2:

if n is even.

then As x>0 increases.

f(x) decreases

and if x<0 decreases.

f(x) decreases.

                                    ⇒If a is positive.

Case 1:

if n is odd.

then As x>0 increases.

f(x) increases.

and if x<0 decreases.

f(x) decreases.

Case 2:

if n is even.

then As x>0 increases.

f(x) increases.

and if x<0 decreases.

f(x) increases.

Hence, the function that best describes the condition:

As x > 0 increases, f(x) increases. As x < 0    decreases, f(x) decreases.

is:

b. odd monomial function with positive a.