1. For which intervals is the function positive?

1.   Since  y  =  f(x)  ,  f(x)  is positive at every point that has a positive  y  value.

 

f(x) is positive when  x  is in the intervals  [-8, -6)  and  (-2, 4) .

 

2.   f(x)  =  x⁵ + 2x

 

To find out if this function is even or odd, we need to find  f(-x) .

 

f(-x)   =   (-x)⁵ + 2(-x)

 

f(-x)   =   - x⁵  -  2x

 

f(-x)   =   (-1)(x⁵ + 2x)

 

f(-x)   =   (-1)( f(x) )

 

Since  f(-x)  =  -f(x) ,  f(x) is an odd function.