How do you know if #x*sin x# is an even or odd function? Precalculus Functions Defined and Notation Introduction to Twelve Basic Functions 1 Answer BeeFree Nov 11, 2015 Even Explanation: A function f is even if the graph of f is symmetric with respect to the y-axis. Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f. Here is graph and note the symmetry with the y-axis : Answer link Related questions What are the twelve basic functions? What is the greatest integer function? What is the absolute value function? What is the graph of the greatest integer function? What is the graph of the absolute value function? What is the inverse function? What is the graph of the inverse function? Which of the twelve basic functions are bounded above? Which of the twelve basic functions are their own inverses? How do you use transformations of #f(x)=x^3# to graph the function #h(x)= 1/5 (x+1)^3+2#? See all questions in Introduction to Twelve Basic Functions Impact of this question 1191 views around the world You can reuse this answer Creative Commons License