What does it mean when a question says if an equation is odd, even, or neither
2 answers:
Even functions are functions that can map onto themselves by a reflection across the y axis
an example is f(x)=x²
odd functions are functions that are reflected across the origin (means one side is flipped across y axis not both sides)
an example is f(x)=x³
to test if it is odd or even or neither, do this test
if it is even, you can replace x with -x and get the same equation
basically if f(x) is an even function then f(x)=f(-x)
exampe
f(x)=x²
f(-x)=(-x)²
f(-x)=x²
same thing, this is even
for an odd one, when you replace x with -x, f(x) turns to -f(x)
basically f(-x)=-f(x)
f(x)=x³
f(-x)=(-x)³
f(-x)=-x³
neither is if it is neither of those like this one
f(x)=x²-2x
if we replace x with -x we get f(-x)=x²+2x and that is not the same function nor is it the negative of the original function
see below
an example is f(x)=x²
odd functions are functions that are reflected across the origin (means one side is flipped across y axis not both sides)
an example is f(x)=x³
to test if it is odd or even or neither, do this test
if it is even, you can replace x with -x and get the same equation
basically if f(x) is an even function then f(x)=f(-x)
exampe
f(x)=x²
f(-x)=(-x)²
f(-x)=x²
same thing, this is even
for an odd one, when you replace x with -x, f(x) turns to -f(x)
basically f(-x)=-f(x)
f(x)=x³
f(-x)=(-x)³
f(-x)=-x³
neither is if it is neither of those like this one
f(x)=x²-2x
if we replace x with -x we get f(-x)=x²+2x and that is not the same function nor is it the negative of the original function
see below
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