Question

How to determine the function is even odd or neither f(x)=5-3x

Answer 1

if the function is mirrored about the y axis, it is even

 use -x in place of x and compare the equations

lets use 2 for x

 so given formula would be 5-3(2) = 5-6 = -1

replace x with -x you would have 5-3(-2) =5-(-6) = 5+6 =11

since -1 does not = 11 the function is neither

even =f(x), odd = -f(x), neither f(x) doesn't equal -f(x)

example of odd:

f(x) = x^5 +x, replace x with -x

f(-x) = (-x)^5 +-x

=-x^5-x

=-(x^5+x)

=-f(x)

ODD

Example of even:

f(x) = 1-x^4

f(-x) = 1-(-x)^4

=1-x^4

=f(x)

EVEN

Example of Neither:

f(x) = 2x-x^2

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

=-(2x+x^2)

does not equal f(x)

NEITHER