Question 402714
1.

One-to-One Function

A function for which {{{every}}} element of the range of the function corresponds to {{{exactly}}}{{{ one}}} element of the domain. One-to-one is often written 1-1.


 Vertical Line Test

A test use to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph at more than one point.



Horizontal Line Test

A test use to determine if a function is one-to-one. If a horizontal line intersects a function's graph more than once, then the function is not one-to-one.



Note: y = f(x) is a function if it passes the vertical line test. It is a {{{1-1 }}}function {{{if}}} it passes {{{both}}} the {{{vertical}}} line test and the {{{horizontal}}} line test. 


A function {{{f}}} from A to B is called {{{one-to-one}}} (or 1-1) if whenever
 {{{f (a) = f (b)}}} then {{{a = b}}}.   No element of B is the image of more than one element in A.


In a one-to-one function, given any y there is only one x that can be paired with the given y.  Such functions are referred to as injective.


A function "{{{f}}} " {{{HAS}}} an {{{INVERSE}}} function " f " {{{if}}} and {{{only}}}{{{ if}}} " f " is {{{one-to-one}}}.


so, check if your function has an inverse:


*[invoke Plot_Inverse_Function "x^2+2x-3", -10, 10, -10, 10]


it does have an inverse, thus it is {{{one-to-one}}}



2.
{{{f(x)= -11x^3+3x^2-x+1}}}, what is the degree of F and what is its leading coefficient? 


1.

The coefficient of the term with the highest degree (greatest power of x) is called the leading coefficient and {{{cannot}}} equal 0.

A polynomial can have any non-negative degree. In other words, the polynomial's degree must be {{{n>= 0}}}.

2.The leading coefficient of a polynomial is the coefficient that is associated with the variable with the highest degree. 

your  polynomial is a polynomial of degree {{{3}}} with leading coefficient {{{-11}}}.