University:
California State University, Northridge
Course:
MATH 150B | Calculus II
Academic year:

2023
Views:

59

Pages:

3
Author:

nadiascoot22

RECALL: From your earlier math courses, you have seen functions that are symmetrical (mirror image) about the y-axis such as the function y = x²: 25 215 105 0.5 005 1 1.5 2 2.5 NEW: There are a number of different terms used to describe the ways in which functions behave. Today, you will learn how to determine whether or not a function's symmetrical behavior is even or odd. neither. CASE 1: EVEN FUNCTIONS An EVEN function is reflected about the y-axis. (signs are the same) An even function satisfies f(-x) = f(x) for all x in its domain Therefore, a function is even if it is unchanged when "x" is replaced by "-x". Example 1: Is f(x) = x² an even function? Let's Check... f(x) = x² C f(-x) = x² f(-x) = (x-) f(-x) = f(x) No signs change. RECALL: From your earlier math courses, you have seen symmetrical functions (mirror image) about the y-axis such as the function y = x²: 25 215 105 0.5 005 1 1.5 2 2.5 NEW: There are a number of different terms used to describe the ways in which functions behave. Today, you will learn how to determine whether or not a function's symmetrical behavior is even or odd. neither. CASE 1: EVEN FUNCTIONS An EVEN function is reflected about the y-axis. (signs are the same) An even function satisfies f(-x) = f(x) for all x in its domain Therefore, a function is even if it is unchanged when "x" is replaced by "-x". Example 1: Is f(x) = x² an even function? Let's Check... f(x) = x² C f(-x) = x² f(-x) = (x-) f(-x) = f(x) No signs change. Therefore, f(x)=x¹ is an odd function since f(-x)=-f(x) CASE 3: NEITHER ODD NOR EVEN f(-x) = f(x) f(-x)-f(x) At least one but not all Signs will change. Example 3: Is f(x) = x²-x odd, even or neither? (signs vary) f(x) = x²-x f(-x) = (-x)² - (-x) 1(-x) = x² + x Therefore, f(-x)f(x) f(x)=x²-x is not even. f(-x)-f(x)f(x) = x²-x is not odd. Therefore, we can conclude that f(x) = x²-x is NEITHER odd nor even.