SOLUTION: Please help me answer and give some explanations as to how to solve this following question: Which of the following relations are one-to-one? Give reasons. 1. 2x

SOLUTION: Please help me answer and give some explanations as to how to solve this following question: Which of the following relations are one-to-one? Give reasons. 1. 2x - 5y =3 2. y^2

Question 760528: Please help me answer and give some explanations as to how to solve this following question: Which of the following relations are one-to-one? Give reasons.
1. 2x - 5y =3
2. y^2 - 3x + 7 =0
3. y= the squareroot of 5-2x
4. y= x^3 -2
5. y= x^2 - 3x +2
6. y= |3x-5|
Thank you in advance and please reply as soon as possible since i need time to learn how to arrive at the answers.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
A one to one function is a function in which every element in the range of the function corresponds with one and only one element in the domain.
Example of a function:
{ (0,1) , (5,2), (6,4) }
Domain: 0, 5, 6
Range: 1,2, 4
Each element in the domain (0, 5, and 6) correspond with a unique element in the range. Therefore this function is a one-to-one function

If a function is , then the function not only passes the vertical line test (the vertical line test is a way to determine whether or not a relation is a function), but it also passes the line test.
The Horizontal Line Test :
If a horizontal line only intersects with the graph of a function once, then this function is . If a horizontal line intersects the graph of the function more than once, then this function is not .
1.

since a horizontal line only intersects with the graph of a function once, function is
2.

since a horizontal line only intersects with the graph of a function once, function is

3.

since a horizontal line only intersects with the graph of a function once, function is
4.

since a horizontal line only intersects with the graph of a function once, function is

5.

since a horizontal line intersects with the graph of a function twice, function is

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