Question

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

Explanation:

Step1: Recall function definition

A relation is a function if each input (x - value) has exactly one output (y - value). So we check each x - coordinate of the points.

Step2: Identify x - values

Let's list the x - coordinates of the points:

• The point on the y - axis has x = 0.
• The point to the right of y - axis (first one) has x = 1.
• The point further right (with lower y) has x = 4.
• The point below the x - axis has x = 1? Wait, no, let's check again. Wait, the points:

Looking at the graph, let's list the (x, y) coordinates:

• (0, y1) (on y - axis)
• (1, y2) (right of y - axis, upper)
• (1, y3) (right of y - axis, lower, below x - axis? Wait, no, the point below x - axis: let's see, the left - most point is ( - 3, y4) (since it's 3 units left of y - axis). Then the point on y - axis: (0, y5). Then (1, y6) (upper), (1, y7) (lower, below x - axis? Wait, no, the point below x - axis: x = 1? Wait, no, let's count the grid. Wait, the key is: does any x - value repeat with different y - values?

Wait, the x - coordinate of 1: is there more than one point with x = 1? Let's see: the point above x - axis with x = 1 (y positive) and the point below x - axis with x = 1 (y negative)? Wait, no, looking at the graph, the points:

• Left - most: x=-3, y negative.
• On y - axis: x = 0, y positive.
• x = 1: two points? Wait, the upper point (x = 1, y positive) and the lower point (x = 1, y negative)? Wait, no, the lower point (below x - axis) has x = 1? Wait, no, maybe I misread. Wait, the graph: let's check the x - coordinates. The points:

1. ( - 3, - 4) (approx, left - most)
2. (0, 4) (on y - axis)
3. (1, 3) (right of y - axis, upper)
4. (1, - 2) (right of y - axis, lower, below x - axis)
5. (4, 2) (further right)
6. (5, 5) (top - right)

Wait, so x = 1 has two different y - values (3 and - 2). Wait, no, maybe I made a mistake. Wait, no, let's look again. Wait, the point below x - axis: is its x - coordinate 1? If so, then x = 1 is associated with two different y - values (one positive, one negative). But wait, maybe I misread the x - coordinate of the lower point. Wait, no, the grid: each square is 1 unit. So the point below x - axis: x = 1 (since it's 1 unit right of y - axis), y negative. And the point above x - axis with x = 1: y positive. So x = 1 has two different y - values. Wait, but that would mean it's not a function. Wait, but maybe I'm wrong. Wait, no, let's check the vertical line test. The vertical line test says that if any vertical line intersects the graph at more than one point, it's not a function. So for x = 1, a vertical line at x = 1 would intersect two points (the upper and lower points with x = 1). Therefore, this relation is not a function. Wait, but wait, maybe I misidentified the x - coordinates. Wait, let's list all points:

• Point 1: x=-3, y=-4 (left - most, below x - axis)
• Point 2: x = 0, y = 4 (on y - axis)
• Point 3: x = 1, y = 3 (above x - axis)
• Point 4: x = 1, y = - 2 (below x - axis)
• Point 5: x = 4, y = 2 (above x - axis)
• Point 6: x = 5, y = 5 (above x - axis)

So x = 1 is used twice with different y - values. Therefore, by the definition of a function (each x has exactly one y), this relation is not a function.

Answer:

no