When you draw graphs from equations, knowing about symmetry can really help you out. Symmetry is when a shape is balanced or looks the same on both sides of a line or point.
Even Functions: An even function, like ( f(x) = x^2 ), is symmetric around the y-axis. This means if you have a point ( (x, f(x)) ), you can also find the point ( (-x, f(x)) ).
Odd Functions: Odd functions, like ( f(x) = x^3 ), are symmetric around the origin. If you have the point ( (x, f(x)) ), you will also have the point ( (-x, -f(x)) ).
Checking for Symmetry: To quickly check for symmetry, you can change ( x ) to ( -x ). If you get ( f(-x) = f(x) ), it’s even. If you get ( f(-x) = -f(x) ), it’s odd.
Examples: For the equation ( y = x^2 ), when you sketch it, you’ll see a U-shape that is centered on the y-axis. For ( y = x^3 ), the curve goes through the origin, showing its odd symmetry.
Understanding symmetry not only makes it easier to draw graphs but also helps you know how the function behaves overall!
When you draw graphs from equations, knowing about symmetry can really help you out. Symmetry is when a shape is balanced or looks the same on both sides of a line or point.
Even Functions: An even function, like ( f(x) = x^2 ), is symmetric around the y-axis. This means if you have a point ( (x, f(x)) ), you can also find the point ( (-x, f(x)) ).
Odd Functions: Odd functions, like ( f(x) = x^3 ), are symmetric around the origin. If you have the point ( (x, f(x)) ), you will also have the point ( (-x, -f(x)) ).
Checking for Symmetry: To quickly check for symmetry, you can change ( x ) to ( -x ). If you get ( f(-x) = f(x) ), it’s even. If you get ( f(-x) = -f(x) ), it’s odd.
Examples: For the equation ( y = x^2 ), when you sketch it, you’ll see a U-shape that is centered on the y-axis. For ( y = x^3 ), the curve goes through the origin, showing its odd symmetry.
Understanding symmetry not only makes it easier to draw graphs but also helps you know how the function behaves overall!