How do you determine if # f(x)=x^4+x^2+3# is an even or odd function?
1 Answer
Apr 27, 2016
even function
Explanation:
To determine if a function is odd/even ,consider the following.
• If f(x) = f( -x) , then f(x) is an even function
Even functions are symmetrical about the y-axis.
• If f( -x) = - f(x) , then f(x) is an odd function.
Odd functions have symmetry about the origin.
Test for even
f( -x)
#=(-x)^4 + (-x)^2 + 3 = x^4 + x^2 + 3 = f(x) # Since f(x) = f( -x) , then function is even
Here is the graph of f(x). Note symmetry about y-axis.
graph{x^4+x^2+3 [-20, 20, -10, 10]}
