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

Algebra ->  Rational-functions -> 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      Log On


   

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) About Me  (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.
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See the graph:
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B2x-3%29
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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
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cheers,
Stan H.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
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+%28a%29+=+f+%28b%29 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:

Solved by pluggable solver: PLOT a FUNCTION and its INVERSE
Plotting a graph:
graph_and_inverse%28+600%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B2x-3+%29
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 one-to-one


2.
f%28x%29=+-11x%5E3%2B3x%5E2-x%2B1, 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%3E=+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.