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Given the graph below, which of the following statements is true? On a coordinate plane, a graph shows an image with three connected lines. The first line has a negative slope and goes from (negative 5, 6) to (negative 2, 0), the second line has a positive slope and goes from (negative 2, 0) to (2, 2), and the third line has a negative slope going from (2, 2) through (4, negative 2). The graph represents a one-to-one function because every x-value is paired with only one y-value. The graph represents a one-to-one function because it is defined for all x-values. The graph does not represent a one-to-one function because it does not pass through the origin. The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

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Answer:

The correct option is (D).

Step-by-step explanation:

A one-to-one function can be defined such the every value of x corresponds to exactly one value of y.

That is:

x₁ → y₁

x₂ → y₂

x₃ → y₃

.

.

.

and so on.

Consider the graph.

From the graph it can be seen that for y = 0 and y = 2 there are multiple x coordinates.

So, the graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

Ver imagen warylucknow

According to the graph it can be concluded that the graph of three lines is not an one one function because the values of 'y' between 0 and 2 are paired with multiple 'x' values.

Given :

  • On a coordinate plane, a graph shows an image with three connected lines.
  • The first line has a negative slope and goes from (-5, 6) to (-2, 0).
  • The second line has a positive slope and goes from (-2, 0) to (2, 2).
  • The third line has a negative slope going from (2, 2) through (4, -2).

Draw the graph of the three lines in order to determine the function is one-one function or not.

The equation of the line passing through (-5,6) and (-2,0) is given by:

[tex]\dfrac{y-6}{x+5}=\dfrac{0-6}{-2+5}[/tex]

[tex]\dfrac{y-6}{x+5}=\dfrac{-6}{3}[/tex]

[tex]y-6=-2(x+5)[/tex]

y + 2x + 4 = 0    --- (1)

The equation of the line passing through (-2,0) and (2,2) is given by:

[tex]\dfrac{y-0}{x+2}=\dfrac{2-0}{2+2}[/tex]

2y = x + 2   ---- (2)

The equation of the line passing through (2,2) and (4,-2) is given by:

[tex]\dfrac{y-2}{x-2}=\dfrac{-2-2}{4-2}[/tex]

y - 2 = -2(x - 2)

y + 2x = 6   ---- (3)

Now, with the help of these three equations, the graph of the three lines can be plotted. The Graph is attached below.

So, according to the graph it can be concluded that the graph of three lines is not an one one function because the values of 'y' between 0 and 2 are paired with multiple 'x' values.

Therefore, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/12465796

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