Question

do the ordered pairs plotted in the graph represent a function? explain your answer.
the graph dropdown a function because dropdown corresponds dropdown one dropdown

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). In other words, for a set of ordered pairs \((x,y)\), no two ordered pairs can have the same \(x\) - value with different \(y\) - values.

Step2: Analyze the x - values of the plotted points

First, identify the \(x\) - coordinates of each plotted point. Let's list the coordinates of the points from the graph:

• Point 1: Let's assume the coordinates (by looking at the grid) are \((- 4,2)\) (x=-4, y = 2)
• Point 2: \((-2,-3)\) (x=-2, y=-3)
• Point 3: \((-2,2)\) (x=-2, y = 2)
• Point 4: \((2,1)\) (x = 2, y=1)
• Point 5: \((4,5)\) (x = 4, y=5)
• Point 6: \((3,5)\) (Wait, no, looking at the grid again, maybe the points are \((-4,2)\), \((-2,-3)\), \((-2,2)\), \((2,1)\), \((4,5)\), \((3,5)\)? Wait, no, the key is to check for repeated \(x\) - values. Wait, the point at \(x=-2\): there are two points with \(x=-2\) (one with \(y = 2\) and one with \(y=-3\))? Wait, no, maybe I misread. Wait, the graph: let's look at the x - axis. The x - values of the points: let's see the blue dots. Let's list their \(x\) and \(y\):

From the grid:

• First dot: x=-4, y = 2
• Second dot: x=-2, y=-3
• Third dot: x=-2, y = 2
• Fourth dot: x=2, y = 1
• Fifth dot: x=3, y = 5
• Sixth dot: x=4, y = 5

Wait, no, maybe the correct points: Wait, the problem is to check if it's a function. A function requires that for each \(x\), there is only one \(y\). So we check if any \(x\) - value is repeated with different \(y\) - values.

Looking at the \(x\) - value of \(-2\): there are two points with \(x=-2\) (one with \(y=-3\) and one with \(y = 2\))? Wait, no, maybe I made a mistake. Wait, the graph: let's count the x - coordinates. Let's see the x - axis labels: -6, -4, -2, 0, 2, 4, 6.

So the points:

• At x=-4: y = 2 (one point)
• At x=-2: is there one or two points? Wait, the blue dots: let's see, the first dot (left) at x=-4, y=2; then at x=-2, maybe two dots? Wait, the problem's graph: let's re - examine. The user's graph: the y - axis is from -6 to 6, x - axis from -6 to 6. The blue dots:

1. (-4, 2)
2. (-2, -3)
3. (-2, 2)
4. (2, 1)
5. (3, 5)
6. (4, 5)

Wait, no, maybe the third dot is at x = - 1? No, the grid lines. Wait, maybe the key is that the x - value of -2 is used twice with different y - values. So, by the definition of a function, if an x - value is associated with more than one y - value, it's not a function.

Wait, but maybe I misread. Wait, the standard vertical line test: if any vertical line intersects the graph at more than one point, it's not a function. So, for x=-2, a vertical line would intersect two points (the ones with y=-3 and y = 2), so the graph does not represent a function because there is an x - value (-2) that corresponds to more than one y - value.

So the first blank: "does not represent", second blank: "there is an x - value that", third blank: "to more than", fourth blank: "y - value".

Answer:

The graph \(\boldsymbol{\text{does not represent}}\) a function because \(\boldsymbol{\text{there is an } x\text{-value that}}\) corresponds \(\boldsymbol{\text{to more than}}\) one \(\boldsymbol{y\text{-value}}\).