[PDF] PRE-CALCULUS Example 1: Write Functions in

How to determine if a function is even/odd?

To determine if a function is even/odd consider the following. Even functions have symmetry about the y-axis. Odd functions have symmetry about the origin. Since f (x) ? f ( -x) , then f (x) is not even. Since f ( -x) ? - f (x) , then f (x) is not odd.

Is F an even function?

SOLUTION (a) The domain of f is , because the absolute value of x exists for every real number x. If x is in , then y y
 x f
x
x 
 x 
f
x. Thus, f is an even function, since f
x
f
x. x (b) Since f is even, its graph is symmetric with respect to the y-axis.

Is the function f(x) = x3 +2x even or odd?

If the function does not satisfy either rule, it is neither even nor odd. Is the function f (x) = x3 +2x f ( x) = x 3 + 2 x even, odd, or neither? Without looking at a graph, we can determine whether the function is even or odd by finding formulas for the reflections and determining if they return us to the original function.

What are the odd and even functions in PDE?

4 October 2017 MATH2065 Introduction to PDEs 3 Even and Odd functions Most functions are neither odd nor even E.g. EVEN EVEN = EVEN (+ + = +) ODD ODD = EVEN (- - = +) ODD EVEN = ODD (- + = -) 4 October 2017 MATH2065 Introduction to PDEs 4