SOLUTION: Please help with the following: 5. Is f(x) = x^2+2x-3 a one-to-one function? Explain your answer 6. For the polynomial f(x)= -11x^3+3x^2-x+1, what is the degree of F and wha

Question 402714: Please help with the following:
5. Is f(x) = x^2+2x-3 a one-to-one function? Explain your answer
6. For the polynomial f(x)= -11x^3+3x^2-x+1, what is the degree of F and what is its leading coefficent?

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
5. Is f(x) = x^2+2x-3 a one-to-one function? Explain your answer
Ans: No. For each x there is only one y-value.
But Some y-values are the result of 2 different x-values.
---
See the graph:

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6. For the polynomial f(x)= -11x^3+3x^2-x+1, what is the degree of F and what is its leading coefficent?
Ans: degree = 3 because the highest power term is x^3
leading coefficient is -11
======================
cheers,
Stan H.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
1.
One-to-One Function
A function for which element of the range of the function corresponds to 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 function it passes the line test and the line test.

A function from A to B is called (or 1-1) if whenever
then . 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 " " an function " f " and " f " is .

so, check if your function has an inverse:

Solved by pluggable solver: PLOT a FUNCTION and its INVERSE

Plotting a graph:

The function is shown in RED and the inverse is snown in GREEN.
This solver uses formula rendering system and here's the actual formula that was plotted:

graph_and_inverse( 600, 400, -10, 10, -10, 10, x^2+2x-3 )

it does have an inverse, thus it is

2.
, 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 equal 0.
A polynomial can have any non-negative degree. In other words, the polynomial's degree must be .
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 with leading coefficient .

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