Question

How do you determine if `y=x^2+1` is an even or odd function?

Answer 1

even function

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) = - fx) then f(x) is odd , `AAx`

Odd functions have symmetry about the origin.

Test for even :

f( -x) `= (-x)^2 + 1 = x^2 + 1 = f(x) " hence even function "`

Here is the graph of function. Note symmetry about y-axis.
graph{x^2+1 [-10, 10, -5, 5]}