How can you tell if a function is even or odd?

If you have a plot of the function, you can look at its symmetries. If the plot to the left of the y axis is the mirror image with respect to the y axis of the plot to the right, it's an even function. If the plot on the left is a mirror image with respect to a diagonal line going from the top left to the top right of your axes system, it is an odd function. (some example plots: f(x)=x2, g(x)=cos(x), ...)If you only have the function's equation, you can try replacing x by -x and see how the function reacts. If f(-x)= f(x), f is an even function, and if f(-x)= -f(x), f is an odd function. For example, (-x)2=x2 and so f(x)=x2 is an even function of x.

FD
Answered by Francois d. Maths tutor

2873 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you find the equation of a tangent to a curve at a certain point, from the equation of the curve?


Solve the simultaneous equations x + y = 1 , x^2 -2xy+y^2=9


A curve has the equation, 6x^2 +3xy−y^2 +6=0 and passes through the point A (-5, 10). Find the equation of the normal to the curve at A.


Find the gradient of y=x^2-6x-16 at the point where the curve crosses the x-axis


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences