Answer:
First choice: (2, 5) (3, 5).
Third choice: (7, -4) (-4, 7) (4, 7)
Fifth choice: (6, 8) (-2, 8) (100, 8), (0.7, 8)
Explanation:
If a(b) is to be a function it must satisfy the vertical line test
What Is Vertical Line Test?
In a vertical line test, you draw a vertical line parallel to the y-axis that cuts the graph. If there is only one point where it cuts the line, then the equation and the graph represent a function
Putting it in other words, there can be only one y-value for a specific x-value. If a single x-value generates more than one y-value it is not function
As an example look at the attached image (this is from the site CueMath)
The graph on the left is y = x² and you can see that any vertical line cuts the graph at only one point. So y = x² is a function
The graph on the right is x = y² and a vertical line drawn will cut the graph at two points so x=y² or equivalently y² = x is not a function
With this knowledge, let's examine each of the 5 choices given
First option: (2, 5) (3, 5).
This can represent a function since for x = 2 there is only one y value and for x = 3 there is only one y value and that is 5. Do not be confused that the y-values are the same for two different x values.
This could represent a horizontal line on the graph
Second option: (5, 2), (5, 3)
This cannot be a function because for the same x value of 5 we get two different y values, 2 and 3
Third option: (7, -4) (-4, 7) (4, 7)
This can represent a function since for any value of x there is a unique value for y. Again it does not matter that -4 and 4 are two different x values which yield the same y value for the reasons specified under option 1
Fourth option: (7, -4) (-4, 7), (-4, -7)
Cannot be a function for reasons stated under option 2. x value of -4 results in two different values for y
Fifth option: (6, 8) (-2, 8) (100, 8), (0.7, 8)
Can represent a function for reasons stated under option 1