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A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

f (x) = x^2 - 2*x

Found in Stewart 7th Ed Section 6.1 #9

Added Mon, 08 Jun '15

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A one to one function is one where every x value has a unique f(x) value.

There are two ways to solve this.

1) By guessing and noticing that both f(0) and f(2) = 0 - which means the function is not one to one

2) or the better way - systematically.

f (x) = x^2 - 2*x

y = x^2 - 2*x

Complete the square to see the problem more clearly (to put it into standard parabolic form)

y + (-2/2)^2 = x^2 - 2*x + (-2/2)^2

Now simplify

y + 1 = x^2 -2x + 1

y + 1 = (x-1)^2

Put into standard form

y - (-1) = (x-1)^2

This tells us that this equation is a parabola with a vertex at -1,-1

As parabolas are not one-to-one functions, this function is not a one to one function.

Added Mon, 08 Jun '15

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