Question

look at this graph: graph of coordinate points is this relation a function? yes no

Explanation:

Step1: Recall the definition of a function

A relation is a function if every input (x - value) has exactly one output (y - value). In other words, no two points in the relation can have the same x - coordinate.

Step2: Analyze the x - coordinates of the points

Let's assume the coordinates of the points (by looking at the grid):
- The left - most point: Let's say its x - coordinate is, for example, \(x=-5\) (assuming the grid lines are 1 unit apart), and y - coordinate is \(y = 1\) (just an example for analysis).
- The next point: \(x=-5\), \(y = 4\) (wait, no, actually, when we look at the graph, we need to check if any two points have the same x - value. Wait, from the graph, let's list the x - coordinates of each black dot. Let's assume the grid is such that each square is 1 unit. Let's identify the x - coordinates:
- The top - left dot: Let's say x=-4, y = 4 (approximate, based on the grid)
- The middle - left dot: x=-5, y = 1
- The lower - middle - left dot: x=-3, y=-1
- The lower - middle - right dot: x=-1, y=-2
- The right - side dot: x = 2, y = 1

Wait, actually, looking at the graph, do any two points have the same x - value? Let's check again. Wait, maybe I misread. Wait, the key is: for a function, each x must map to only one y. So we check if there are two points with the same x. Let's look at the x - coordinates of each point. Let's assume the x - coordinates (from left to right):

First point (left - most, middle): x=-5 (let's say), y = 1

Second point (top - left): x=-4, y = 4

Third point (middle - left, lower): x=-3, y=-1

Fourth point (lower - middle): x=-1, y=-2

Fifth point (right - side): x = 2, y = 1

Wait, no, maybe I made a mistake. Wait, actually, when we look at the graph, are there any two points with the same x - coordinate? Let's check the x - values. Let's suppose the grid is such that each vertical line is an integer x - value. So, for each black dot, we check its x - coordinate. If all x - coordinates are unique, then it is a function.

Wait, maybe the initial analysis was wrong. Wait, let's think again. The definition of a function is that for every x in the domain, there is exactly one y in the range. So we need to check if any two points have the same x - value. Let's look at the graph:

Looking at the five black dots, do any two have the same x - coordinate? Let's assume the x - coordinates (from left to right):

1. Left - most dot: x=-5 (let's say), y = 1

2. Top - left dot: x=-4, y = 4

3. Middle - left (lower) dot: x=-3, y=-1

4. Lower - middle dot: x=-1, y=-2

5. Right - side dot: x = 2, y = 1

Wait, so all x - coordinates are different (-5, -4, -3, -1, 2). So each x has only one y. Therefore, this relation is a function. Wait, but maybe I misread the graph. Wait, maybe the left - most dot and another dot have the same x? Wait, no, from the graph, the left - most dot (middle y) and the top - left dot (top y) have different x - coordinates. Wait, maybe the user's graph has points with unique x - values. So according to the vertical line test: if we draw a vertical line through any x - value, it should intersect the graph at most once. Since all x - coordinates are unique, the vertical line test is passed. So the relation is a function.

Wait, but maybe I made a mistake. Wait, let's check again. Let's list the x - coordinates:

- The dot on the left (middle y): x=-5 (let's say)

- The dot above it (top y): x=-4

- The dot below the left - middle (lower y): x=-3

- The dot to the right of that (lower - middle): x=-1

- The dot on the right (middle y): x = 2

All x - values are distinct. So each x has one y. So the relation is a function. So the answer is yes.

Answer:

yes