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

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. <embed type="image/svg+xml" src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg" style="width: 300px; height: 200px; vertical-align: middle; float: none;" sscr="-7.5,7.5,-5,5,1,1,1,1,1,300,200,func,x^2-x+1,null,0,0,,,black,1,none" /> (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.

Homework Help > Math

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

Print
document PDF
Cite

Expert Answers

embizze

| Certified Educator

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.

Cite
Link