Is the function h(x)=x3−5 even, odd or neither?
1 Answer
May 23, 2016
neither
Explanation:
To determine if a function is even/odd consider the following.
• If f(x) = f( -x) , then f(x) is even
Even functions are symmetrical about the y-axis.
• If f( -x) = - f(x) , then f(x) is odd
Odd functions are symmetrical about the origin.
Test for even
f(−x)=(−x)3−5=−x3−5≠f(x) Since f(x) ≠ f( -x) , then f(x) is not even.
Test for odd
−f(x)=−(x3−5)=−x3+5≠f(−x) Since f( -x) ≠ - f(x) , then f(x) is not odd.
hence f(x) is neither even nor odd.
graph{x^3-5 [-20, 20, -10, 10]}
