F(x)=3x+7 even odd or neither determine algebraically

A function is an "even" function if  f(x) = f(-x)  for all values of x.

A function is an "odd" function if  f(-x) = -f(x) for all values of x.

 

Choose a value for x; 2 is OK:

f(2)  =  3(2) + 7  =  13                                 --->  -f(2)  =  -13

f(-2) =  3(-2) + 7  =  1

Since  f(2) ≠ f(-2), it can't be even.

Since  f(-2) ≠ -f(2), it can't be odd.