Is the function #y=x^4# odd, even, or neither?
2 Answers
It is even. See explanation.
Explanation:
To check if a function is even, odd or neither you have to calculate
-
if
#f(-x)=f(x)# then the function is even, -
if
#f(-x)=-f(x)# then the function is odd, -
in other cases the function is neither odd or even.
Here we have:
#f(x)=x^4#
Note:
Generally the function
Other way of checking if the function is odd or even is to look at its graph:
The
graph{x^2 [-10, 10, -5, 5]}
If a function is even then the origin is its center of symetry:
graph{x^5 [-10,10,-5,5]}
Explanation:
#"to determine if y is odd/even"#
#• " 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 have half turn symmetry about the origin"#
#f(-x)=(-x)^4=x^4=f(x)#
#rArry=x^4" is even"#
graph{x^4 [-10, 10, -5, 5]}