Question 57873This question is from textbook College Algebra
: 11. is the function f(x)=x^5+4x-7 even, odd, or neither?
12. determine the intervals over which f(x)=(x^2-4)^2 is increasing, decreasing, or constant.
This question is from textbook College Algebra
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! 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:
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!!!
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