Which graph is a one-to-one function

The graph which is a one-to-one function is:

                      Graph B

Step-by-step explanation:

Function--

The graph of a function must always pass the vertical line test i.e. any line passing through the domain and parallel to the y-axis must pass through the graph exactly once.

and also for a function to be one-one the graph of the function must pass horizontal line test i.e. any line passing through the co-domain and parallel to the x-axis must intersect the graph at most once.

In the given graphs :

Graph A is not a function, since it does not pass the horizontal line test and hence we won't talk about being a one-one function.

Graph B is a function as well is one-one since it passes horizontal as well as  vertical line  test.

Graph C is a function but is not one-one as it fails the horizontal line test.

               Hence, the correct answer is:

                          Graph B

Discriminant: b² - 4ac = - 8 (no real solutions)

Step-by-step explanation:

We are given the following quadratic equation, 3x² + 2x + 1 = 0, where a = 3, b = 2, and c = 1.

In the Quadratic Formula, , the expression under the radical symbol, "b² - 4ac" is the discriminant, which tells us the number of solutions of a given quadratic equation.  When we substitute the values for a, b, and c of a given quadratic equation into the quadratic formula, we are essentially solving for its number of solutions.

Discriminant: b² - 4acIf b² - 4ac > 0, then it means that the quadratic equation has two real solutions. If b² - 4ac = 0, then it means that the quadratic equation has one real solution.If b² - 4ac < 0, then it means that the quadratic equation has no real solutions. Solution:

Given the quadratic equation, 3x² + 2x + 1 = 0, where a = 3, b = 2, and c = 1, let us substitute the values for a, b, and c into the discriminant to determine its number of solutions:

Discriminant:  b² - 4ac =  (2)² - 4(3)( 1 ) = 4 - 12 = - 8

Hence, the discriminant of 3x² + 2x + 1 = 0 is -8, which means that the given quadratic equation has no real solutions.  This implies that the 3x² + 2x + 1 = 0 has no x-intercepts (because the graph does not cross the x-axis).  

Attached is a screenshot of the graphed quadratic equation, 3x² + 2x + 1 = 0, where it shows that it does not cross the x-axis, proving that there are no real solutions.