Even and odd functions have unique patterns in their graphs. They mirror across different lines.
Even Functions: These functions look the same when you flip them over the y-axis (the vertical line in the middle of the graph). For an even function, like ( f(x) ), it follows this rule: ( f(x) = f(-x) ). A simple example is ( f(x) = x^2 ). Here, if you plug in 2, you get ( f(2) = 4 ). If you plug in -2, you still get ( f(-2) = 4 ).
Odd Functions: These functions have a twisty pattern when you turn them around the origin (the center point where the x and y axes cross). For an odd function, the rule is: ( f(-x) = -f(x) ). A popular example is ( f(x) = x^3 ). For this function, when you put in 2, you get ( f(2) = 8 ). But when you put in -2, you get ( f(-2) = -8 ).
Understanding these types of functions helps you know how their graphs will look. It’s very useful when you study functions!
Even and odd functions have unique patterns in their graphs. They mirror across different lines.
Even Functions: These functions look the same when you flip them over the y-axis (the vertical line in the middle of the graph). For an even function, like ( f(x) ), it follows this rule: ( f(x) = f(-x) ). A simple example is ( f(x) = x^2 ). Here, if you plug in 2, you get ( f(2) = 4 ). If you plug in -2, you still get ( f(-2) = 4 ).
Odd Functions: These functions have a twisty pattern when you turn them around the origin (the center point where the x and y axes cross). For an odd function, the rule is: ( f(-x) = -f(x) ). A popular example is ( f(x) = x^3 ). For this function, when you put in 2, you get ( f(2) = 8 ). But when you put in -2, you get ( f(-2) = -8 ).
Understanding these types of functions helps you know how their graphs will look. It’s very useful when you study functions!