* Function : f (x) = y
EVEN FUNCTIONS
When a function is even the input(x) whether it be positive or negative it will ALWAYS have the same output (y) .
algebraically speaking: f (x) = f (-x)
Example: #1
f (x) = x² . ....................................... f (-x) = (-x) ²
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;.........f (-x) = x²
Example: #2
f (x) =x ^4 + 2 .................................. f (-x) = (-x) ^ 4 +2
................................................... f (-x) = x^4 +2
NOTICE:SAME OUTPUT
(wheter the input is + or - )
HINT: Usually when the input has an even exponent or it is absolute valued it is an even function
When you graph an even function it is symmetrical about the y-axis
When a function is odd the output (y) of a negative input(-x) is the same output (y) of a positive input (x) when you times the positive input's output by (-1)
algebraically speaking : f (-x) = - f(x)
Example: #1
f (-x) = (- x) ....................................... -f (x) = x
f (-x) = -x .......................................... f (x)= -x
f (-x) = -x .......................................... f (x)= -x
Example: #2
f (-x) = (- x)³................................................-f (x) = x³
f (-x) = -x ³ ................................................... f (x)= -x ³
NOTICE: SAME OUTPUT
f (-x) = -x ³ ................................................... f (x)= -x ³
NOTICE: SAME OUTPUT
HINT: Usually when the inout has an odd exponent it is an odd function
When you graph an odd function it is symmetrical about the origin
I still don't get the whole positive/negative input or output thing... I mean, I get how even and odd functions work but when people include things about the output I get lost... I think it's because of the fancy words that are involved in the explanations... XD
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