Determine whether the function is even, odd, or neither. a) y=5x3-2x b) f(x)=3x4-2x2

Answer 1

a) is odd

b) is even

to be odd f(-x) = -f(x)

y = f(x) = 5x3 -2x

f(-x) = 5(-x)^3 -2(-x)

= -5x^3+2x

= -(5x^3 -2x)

= -f(x)

graph them: f(x) is symmetrical about the y axis to f(-x)

f(x) is reflected about the y axis to get f(-x)

rotate f(x) about the origin, and it becomes f(-x)

to be even f(-x) = f(x)

y = f(x) =3x^4 -2x^2

f(-x) = 3(-x)^4 -2(-x)^2

= 3x^4-2x^2

= f(x)

f(x) and f(-x) are symmetrical about the origin

rotate f(x) about the y axis, and it becomes f(-x)