Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. the graph represents a function. which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function? (3, 0) (2, -3) (-2, 1) (-3, -1)

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). So, we need to check the x - values of the given points and the options.
First, let's identify the x - values of the existing four points from the graph. Let's assume the four points (from the blue dots) have x - values: let's see the grid, suppose the points are, for example, ( - 4,1), ( - 2, - 2), (3,2), (3, - 1) (wait, no, wait, the x - values: let's check the options. Wait, the options are (3,0), (2, - 3), ( - 2,1), ( - 3, - 1). Let's check the x - values of the existing points. Let's look at the x - coordinates: from the graph, the x - values of the four points: let's see, one is at x=-4, one at x = - 2, one at x = 3, one at x = 3? Wait, no, if x = 3 has two points, that can't be a function. Wait, maybe I misread. Wait, the problem says "the graph represents a function", so the existing four points must have unique x - values. Wait, maybe the four points have x - values: let's check the options. Let's list the x - values of the options: 3, 2, - 2, - 3.

Step2: Check each option's x - value against existing x - values

• Option 1: \((3,0)\): If there is already a point with x = 3 (from the graph, since one of the blue dots is at x = 3), then adding (3,0) would mean x = 3 has two y - values (the existing one and 0), so it's not a function.
• Option 2: \((2, - 3)\): Let's check if x = 2 is already used. From the graph, do we have a point with x = 2? The existing points: let's see, the x - values of the four points: suppose the four points have x - values - 4, - 2, 3, and another? Wait, maybe the four points are ( - 4,1), ( - 2, - 2), (3,2), (3, - 1) no, that can't be, because x = 3 would be repeated. Wait, no, the graph is a function, so x - values are unique. So maybe the four points have x - values: - 4, - 2, 3, and let's say another x. Wait, maybe I made a mistake. Wait, let's check the x - value of (2, - 3). Is x = 2 already in use? Let's assume the existing points: if there is no point with x = 2, but wait, let's check the other options.
• Option 3: \((-2,1)\): If there is a point with x=-2 (from the graph, one of the blue dots is at x = - 2), then adding (-2,1) would mean x=-2 has two y - values, so not a function.
• Option 4: \((-3, - 1)\): The x - value is - 3. Check if x=-3 is already used. From the existing four points, the x - values are not - 3 (since the existing x - values are - 4, - 2, 3, and maybe another, but - 3 is new). So adding (-3, - 1) means x=-3 has only one y - value (-1), so it's a function.

Answer:

\((-3, -1)\)