Sketch the following functions/relations and supply the domain and range. (continued...)

If it is afunction, state whether it is into, onto or one to one from R ---> R and justify.

y = x^2 – x +1

Expert Answers

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Sketch `y=x^2-x+1` . If it is a function, state the domain and range and determine if it is onto, one-to-one, or both.

(1) This is a function -- it is a parabola.

(2) The domain is all real numbers as all polynomials have this domain. The range is y>3/4. The parabola has a minimum value at its vertex (1/2,3/4).

(3) This function is neither injective (one-to-one) nor surjective (onto), and thus not bijective (both).

It is not one-to-one since the graph fails the horizontal line test. For example, if y=3 x=2 or -1.

It is not onto since the function never maps to a negative number.

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