Identifying Functions | Graphs worksheet with nine graphs to determine if each represents a function.

Let’s go through each graph one by one to decide if it represents a function.

Remember: A graph is a function if every x-value (input) has only one y-value (output). You can use the “vertical line test” — imagine drawing vertical lines across the graph. If any vertical line touches the graph in more than one place, then it’s not a function.

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Graph 1:
This curve goes down and to the right. If you draw any vertical line, it will hit the graph only once. So yes — this is a function.

Graph 2:
It’s a wavy line going up and down. But no matter where you put a vertical line, it only hits the graph once. So yes — this is a function.

Graph 3:
Looks like a shallow U-shape opening upward. Vertical lines will only touch it once. So yes — this is a function.

Graph 4:
This is an S-shaped curve that bends left and right. Try drawing a vertical line near the middle — it might hit the graph in two places! For example, at x = -5, there are two different y-values. So no — this is not a function.

Graph 5:
Straight diagonal line going down. Every vertical line hits it exactly once. So yes — this is a function.

Graph 6:
This is an oval or ellipse. Draw a vertical line through the center — it hits the top and bottom of the oval. That means one x-value gives two y-values. So no — this is not a function.

Graph 7:
Two separate curves — one on the left, one on the right. Each part passes the vertical line test. Even though they’re disconnected, as long as no single x-value has two outputs, it’s okay. Check carefully — for example, at x = -8, only one point; at x = 8, only one point. No overlaps vertically. So yes — this is a function.

Wait — let me double-check Graph 7. Look at x = 0 — nothing there. At x = 5? Only one point on the right curve. At x = -5? Only one point on the left curve. There’s no x-value that appears in both curves with different y-values. So still — yes, it is a function.

Graph 8:
A straight line segment going up. Vertical lines hit it only once. So yes — this is a function.

Graph 9:
This looks like a step or L-shape. From x=0 to x=10, it’s flat at y=20. Then from x=10 onward, it drops to y=0 and stays there. Wait — what happens at x=10? It seems to have two points: one at (10,20) and one at (10,0)? Actually, looking closely — the graph shows a solid dot at (10,20) and maybe an open circle or just a corner? In most cases like this, if it’s drawn as a continuous jump without overlapping, we assume each x has only one y. But here — at x=10, does it have two values?

Actually, re-examining: The graph starts at (0,20), goes right to (10,20), then drops straight down to (10,0), then goes right along y=0. So at x=10, there are TWO points: (10,20) and (10,0). That means one input (x=10) has two outputs → NOT a function.

But wait — sometimes graphs use open/closed circles to show which point is included. Since this image doesn’t clearly mark them, but visually, it looks like both points exist at x=10. So we must say: not a function.

Alternatively, if the drop is instantaneous and only one point is meant to be at x=10, it could be ambiguous. But based on standard interpretation of such diagrams in worksheets, if a vertical line hits two points, it’s not a function. Here, at x=10, it definitely hits two distinct points. So — not a function.

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Final check:

1) Yes
2) Yes
3) Yes
4) No
5) Yes
6) No
7) Yes
8) Yes
9) No

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Final Answer:
1) Yes
2) Yes
3) Yes
4) No
5) Yes
6) No
7) Yes
8) Yes
9) No