Determine if Odd, Even, or Neither f(x)=-9x^4+5x+3

Problem

ƒ(x)=−9*x4+5*x+3

Solution

1. Recall the definitions for function parity: a function is even if ƒ*(−x)=ƒ(x) and odd if ƒ*(−x)=−ƒ(x)

2. Substitute −x for every instance of x in the original function.

ƒ*(−x)=−9*(−x)4+5*(−x)+3

3. Simplify the powers and products, noting that (−x)4=x4

ƒ*(−x)=−9*x4−5*x+3

4. Compare the result to the original function ƒ(x)=−9*x4+5*x+3 Since −9*x4−5*x+3≠−9*x4+5*x+3 the function is not even.

5. Compare the result to the negative of the original function −ƒ(x)=9*x4−5*x−3 Since −9*x4−5*x+3≠9*x4−5*x−3 the function is not odd.

Final Answer

ƒ(x)=−9*x4+5*x+3* is Neither

Want more problems? Check here!