Algebra 1 Worksheets | Domain and Range Worksheets - Free Printable

Let’s go through each graph one by one to find the Domain, Range, and whether it’s a Function.

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What do these terms mean?

- Domain: All the x-values (left to right) that the graph covers.
- Range: All the y-values (bottom to top) that the graph covers.
- Function: A graph is a function if every x-value has only ONE y-value. You can check this with the vertical line test — if any vertical line hits the graph more than once, it’s NOT a function.

We’ll look at each graph and write:

- Domain: from smallest x to largest x (use interval notation or inequalities)
- Range: from smallest y to largest y
- Function: Yes or No

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## Graph 1:
Looks like a short curve going from x=2 to x=4, y=3 to y=5.

- Domain: x from 2 to 4 → [2, 4]
- Range: y from 3 to 5 → [3, 5]
- Function? Yes — passes vertical line test.

✔ Domain: [2, 4]
✔ Range: [3, 5]
✔ Function: Yes

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## Graph 2:
Semi-circle opening downward, from x=-4 to x=4, but not including endpoints (open circles).

- Domain: x from -4 to 4, not including ends → (-4, 4)
- Range: y from 0 to 3, not including 0? Wait — bottom is at y=0 (open circle), top at y=3 (closed? Actually, looks like both ends are open). Let’s check: left end at (-4,0) open, right end at (4,0) open, peak at (0,3) — probably closed? But in the image, it looks like all endpoints are open. Hmm.

Actually, looking again: the curve starts at (-4,0) open, goes up to (0,3) — which seems solid? Or is it open? The problem doesn’t specify, but typically in such graphs, if it’s drawn as a smooth arc with open circles at ends, we assume the middle is included.

But to be safe — let’s say:

- Domain: (-4, 4)
- Range: (0, 3] — assuming top point is included (since no open circle there)
Wait — actually, in the image, the top point at (0,3) also has an open circle? Hard to tell. Let me re-express based on standard interpretation.

Actually, in most worksheets like this, if the endpoint is not filled, it’s excluded. Looking at graph 2: both ends at y=0 are open, and the top at y=3 — if it’s a semicircle, likely the top is included unless marked open. But since it’s not clearly marked, and to match common practice, I’ll assume:

Domain: (-4, 4)
Range: (0, 3] — because the highest point is reached and not open? Wait — actually, in the image, the top point might be open too. This is ambiguous.

To resolve: Let’s assume the graph is continuous between the open endpoints. So:

If the curve is drawn from (-4,0) open to (4,0) open, peaking at (0,3) — and if (0,3) is not marked open, then it’s included.

But in many such problems, they use open circles to indicate exclusion. Since only the ends have open circles, and the top doesn’t, we’ll include y=3.

So:

✔ Domain: (-4, 4)
✔ Range: (0, 3]
✔ Function: Yes — still passes vertical line test.

Wait — actually, looking again: in graph 2, the entire curve is drawn with open circles at both ends, and the top point is just part of the curve — no special marking. In math, if a point is on the curve and not marked open, it’s included. So yes, y=3 is included.

But let’s double-check with the vertical line test — yes, it’s a function.

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## Graph 3:
Wavy line from x=-4 to x=3, with open circle at (-4,-2) and open circle at (3,5).

- Domain: x from -4 to 3, not including ends → (-4, 3)
- Range: lowest y is -2 (but open), highest is 5 (open) — but does it go below -2? At x=-4, y=-2 open, and the curve goes up and down — minimum y seems to be around -2, maximum around 5. But since endpoints are open, and the curve doesn’t reach lower than -2 or higher than 5, range is (-2, 5)

Wait — actually, at x=0, y=0; at x=1, y=-1; at x=2, y=0; at x=3, y=5 open. And at x=-4, y=-2 open. Does it go below -2? Doesn’t seem so. So range is (-2, 5)

Function? Yes — no vertical line hits twice.

✔ Domain: (-4, 3)
✔ Range: (-2, 5)
✔ Function: Yes

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## Graph 4:
Leftward opening parabola-like shape, from x=-5 to x=0, with open circles at (-5,0) and (0,-3) and (0,3)? Wait — actually, it’s symmetric over x-axis? From x=-5 to x=0, and for each x, two y-values? Yes!

At x=-5, y=0 (open); at x=0, y=3 and y=-3 (both open). So for example, at x=-2, there are two points: one above x-axis, one below.

So:

- Domain: x from -5 to 0, not including ends → (-5, 0)
- Range: y from -3 to 3, not including ends → (-3, 3)
- Function? NO — fails vertical line test (e.g., at x=-2, two y-values)

✔ Domain: (-5, 0)
✔ Range: (-3, 3)
✔ Function: No

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## Graph 5:
A sideways parabola, opening to the right, vertex at (0,0), from x=0 to x=4, with open circles at (0,3) and (0,-3)? Wait — actually, it starts at (0,3) open, goes to (4,0), and to (0,-3) open? So it’s symmetric over x-axis.

For each x>0, two y-values (positive and negative). So not a function.

- Domain: x from 0 to 4, not including 0? Open circles at (0,3) and (0,-3), so x=0 is excluded? But the curve includes x>0. Actually, the leftmost point is at x=0, but open, so domain is (0, 4]

Wait — the graph goes from x=0 (open) to x=4 (included? At (4,0) — is it open or closed? In the image, it looks like (4,0) is a solid point? Or open? Let’s assume (4,0) is included since not marked open.

But at x=0, both ends are open, so x=0 not included.

So:

- Domain: (0, 4]
- Range: y from -3 to 3, not including -3 and 3? Because at x=0, y=±3 are open, and at x=4, y=0 — so range is (-3, 3)

Function? No — vertical line test fails.

✔ Domain: (0, 4]
✔ Range: (-3, 3)
✔ Function: No

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## Graph 6:
Straight line with positive slope, from bottom-left to top-right. Passes through origin? Looks like from (-3,-6) to (3,6), both ends included? Or open? In the image, endpoints seem solid.

Assume closed endpoints.

- Domain: x from -3 to 3 → [-3, 3]
- Range: y from -6 to 6 → [-6, 6]
- Function? Yes — straight line, passes vertical line test.

✔ Domain: [-3, 3]
✔ Range: [-6, 6]
✔ Function: Yes

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## Graph 7:
Straight line with negative slope, from (-4,2) open to (2,-4) open.

- Domain: x from -4 to 2, not including ends → (-4, 2)
- Range: y from -4 to 2, not including ends → (-4, 2)
- Function? Yes — straight line, one y per x.

✔ Domain: (-4, 2)
✔ Range: (-4, 2)
✔ Function: Yes

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## Graph 8:
Sideways parabola opening to the right, vertex at (0,0), from x=0 to x=4, with open circles at (0,3) and (0,-3)? Similar to graph 5 but different scale.

From x=0 (open) to x=4 (open? At (4,3) and (4,-3) — both open). So:

- Domain: (0, 4)
- Range: y from -3 to 3, not including ends → (-3, 3)
- Function? No — for each x>0, two y-values.

✔ Domain: (0, 4)
✔ Range: (-3, 3)
✔ Function: No

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Now, let’s compile all answers neatly.

Final Answer:

1) Domain: [2, 4], Range: [3, 5], Function: Yes
2) Domain: (-4, 4), Range: (0, 3], Function: Yes
3) Domain: (-4, 3), Range: (-2, 5), Function: Yes
4) Domain: (-5, 0), Range: (-3, 3), Function: No
5) Domain: (0, 4], Range: (-3, 3), Function: No
6) Domain: [-3, 3], Range: [-6, 6], Function: Yes
7) Domain: (-4, 2), Range: (-4, 2), Function: Yes
8) Domain: (0, 4), Range: (-3, 3), Function: No

Note: For graph 2, if the top point (0,3) is also open, then range would be (0,3). But based on typical worksheet conventions, since it's not marked open, we include it. If your teacher specifies otherwise, adjust accordingly.

But to match common textbook style, I'll keep range as (0,3] for graph 2.

However, upon closer inspection of the original image (as described), in graph 2, the entire curve is drawn with open circles at the two ends, and the top point is just a point on the curve — no open circle, so it should be included. So (0,3] is correct.

Similarly, for graph 5, at x=4, the point (4,0) — if it's not marked open, it's included, so domain (0,4].

All good.

Final Answer:

1) Domain: [2, 4], Range: [3, 5], Function: Yes
2) Domain: (-4, 4), Range: (0, 3], Function: Yes
3) Domain: (-4, 3), Range: (-2, 5), Function: Yes
4) Domain: (-5, 0), Range: (-3, 3), Function: No
5) Domain: (0, 4], Range: (-3, 3), Function: No
6) Domain: [-3, 3], Range: [-6, 6], Function: Yes
7) Domain: (-4, 2), Range: (-4, 2), Function: Yes
8) Domain: (0, 4), Range: (-3, 3), Function: No