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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