Question

Identify the monomial function described as odd or even, and indicate whether a is positive or negative.

Answer 1

Identify the monomial function described as odd or even, and indicate whether a is positive or negative.

Answer 2

Answer:

Case 1: As x > 0 increases, f(x) increases.  As x < 0 decreases, f(x) decreases.

It is an 'odd' function with 'positive' a.

Case 2: As x > 0 increases, f(x) decreases.  As x < 0 decreases, f(x) decreases.

It is an 'even' function with 'negative' a.

Case 3: As x > 0 increases, f(x) increases.  As x < 0 decreases, f(x) increases.

It is an 'even' function with 'positive' a.

Case 4: As x > 0 increases, f(x) decreases.  As x < 0 decreases, f(x) increases.

It is an 'odd' function with 'negative' a.

Step-by-step explanation:

Let us consider a monomial function:

             f(x) = axⁿ

Case 1:

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

This happens only if a is 'positive' and n is 'odd'.  So, it is an 'odd' function with 'positive' a.

Case 2:

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

This happens only if a is 'negative' and n is 'even'. So, it is an 'even' function with 'negative' a.

Case 3:

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

This happens only if a is 'positive' and n is 'even'. So, it is an 'even' function with 'positive' a.

Case 4:

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

This happens only if a is 'negative' and n is 'odd'. So, it is an 'odd' function with 'negative' a.

Keywords: monomial function, odd function, even function

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