Question 213488
if every value of x yield one and only one value of y, the equation is a function.
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f(x) = x^2 + 2x - 3 is a function.
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let y = f(x) and we can graph this equation.
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{{{graph (300,300,-10,10,-10,10,x^2 + 2x - 3)}}}
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if f(a) equals f(b), this does not mean the equation is not a function.
you would have one value of y for 2 values of x.
f(x1) would be y
f(x2) would be y
you still only have one value of y for each value of x so the equation is still a function.
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the definition of a function is one value of f(x) for each value of x.
f(a) = f(b) does not violate this.
take y = x^2
let a = 2
then f(a) = 4
let b = -2
then f(b) = 4
f(2) = f(-2)
you have f(a) = f(b) but you still only have one value of y for each value of x.
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