How do you determine if #f(x) = 2x^5 - 3x^2 + 2 # is an even or odd function?
1 Answer
Mar 28, 2016
Neither
Explanation:
To determine if a function is even/odd the following applies.
• If f(x) = f( -x) then f(x) is even ,
#AAx # Even functions have symmetry about the y-axis.
• If f( -x) = - f(x) then f(x) is odd ,
#AAx # Odd functions have symmetry about the origin.
#"----------------------------------------------------------------"# Test for even :
f( -x)
#= 2(-x)^5 - 3(-x)^2 + 2 = -2x^5 - 3x^2 + 2# since f(x) ≠ f( -x) , then f(x) is not even.
#"-----------------------------------------------------------"# Test for odd :
# -f(x) = -(2x^5 - 3x^2 + 2) = -2x^5 + 3x^2 - 2 # since -f(x) ≠ f( -x) , then f(x) is not odd.
