Question 57873
11. is the function f(x)=x^5+4x-7 even, odd, or neither?
If f(-x)=f(x) the function is even.
If f(-x)=f(x)  the function is odd
f(-x)=(-x)^5+4(-x)-7
f(-x)=-x^5-4x-7  <---Neither
:
A short cut is to look at all of the exponents of the variables, think of any constants like -7 as being -7x^0.  If all of the exponents are even, the function is even, if all of the exponents are odd, the function is odd, if there is a mixture of any kind, it's neither.  
The variables of this equation are, 5,1, and 0.  Neither. 

12. determine the intervals over which f(x)=(x^2-4)^2 is increasing, decreasing, or constant.
If you are in calculus, you find this out through taking derivatives.  Let me know if that's the case:
If you're in algebra or algebra II the  most teachers are content to let you use your graphing calculators to solve these, using the max, min functions.
Here's the graph:
{{{graph(300,200,-5,5,-5,20,(x^2-4)^2)}}}
As you can see, 
the Graph is increasing from x=(-2,0)U(2,infinity)
The graph is decreasing from x=(-infinity,-2)U(0,2)  
Happy Calculating!!!