Identify numbers as even or odd

Learning Objectives Define even and odd numbers using the algebraic forms 2k and 2k+1. Determine the parity (evenness or oddness) of the result of arithmetic operations on integers. Evaluate the parity of a polynomial expression for an integer input without direct calculation. Algebraically identify a function as even by testing if f(-x) = f(x). Algebraically identify a function as odd by testing if f(-x) = -f(x). Distinguish between even, odd, and functions that are neither. Connect the algebraic properties of even and odd functions to the symmetry of their graphs. Ever notice how the graph of y = x² is perfectly symmetrical across the y-axis, but y = x³ is not? 🤔 This symmetry is directly related to the concepts of 'even' and 'odd' applied to functio...

TermDefinitionExample ParityThe property of an integer of being either even or odd. It is a fundamental concept in number theory.The number 17 has a parity of 'odd'. The number -4 has a parity of 'even'. Even Number (Algebraic Form)An integer 'n' that can be expressed in the form n = 2k, where 'k' is any integer.The number 12 is even because it can be written as 2 * 6. Odd Number (Algebraic Form)An integer 'n' that can be expressed in the form n = 2k + 1, where 'k' is any integer.The number -9 is odd because it can be written as 2 * (-5) + 1. Even FunctionA function f(x) for which f(-x) = f(x) for all x in its domain. The graph of an even function is symmetric with respect to the y-axis.f(x) = x² is an even function because f(-x)...

Rules of Parity for Operations Let E be an even integer and O be an odd integer. Then: E ± E = E, O ± O = E, E ± O = O. Also: E * (any integer) = E, O * O = O. Use these rules to quickly determine the parity of a complex arithmetic expression without calculating the final value. This is especially useful in algebra. Rule of Parity for Integer Powers Let O be an odd integer and E be an even integer. For any positive integer n: O^n = O, E^n = E. This rule simplifies determining the parity of terms with exponents. An odd number multiplied by itself any number of times will always be odd. The Function Parity Test Given a function f(x): 1. Calculate f(-x). 2. If f(-x) = f(x), the function is EVEN. 3. If f(-x) = -f(x), the function is ODD. 4. If neither is true, the function...