Function Worksheets - Free Printable

Explanation:
We need to find the domain and range of each graph.

- Domain = all possible *x*-values (horizontal direction) that the graph covers.
- Range = all possible *y*-values (vertical direction) that the graph covers.

We read these from the graph by looking at the leftmost and rightmost points for domain, and the lowest and highest points for range. If the graph has endpoints (dots), those values are included; if it goes on forever (arrow), we use ∞ or −∞.

Let’s go one by one:

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1) Graph is a curve starting at x = −10 (closed dot) and going right to x = −2 (open dot). So:
- Domain: from −10 to −2, including −10 but not −2 → [−10, −2)
- y-values go from y = 3 (at x = −10) up to y = 15 (at x = −2, open, so y = 15 not included) → Range: [3, 15)

Wait — check graph carefully: At x = −10, y = 3 (solid dot). Curve rises to near x = −2, y = 15, but open circle at (−2, 15), so y never reaches 15. Lowest y is 3, highest approaches 15. So yes:
Domain: [−10, −2)
Range: [3, 15)

But let me double-check coordinates: The grid shows x-axis labeled −16 to 8, y from −4 to 20. Point at x = −10, y = 3 (solid). Then curve goes up and right, ending with open circle at x = −2, y = 15. Correct.

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2) Straight line from upper left to lower right. It has arrowheads on both ends → continues forever in both directions. So:
- Domain: all real numbers → (−∞, ∞)
- Range: also all real numbers → (−∞, ∞)

Check: Line passes through (−6, 20) and (6, −10)? Actually, from graph: when x = −6, y = 20; x = 6, y = −10 — but since arrows go both ways, yes, infinite.

So Domain: (−∞, ∞), Range: (−∞, ∞)

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3) Curve: starts at (−2, 0) — solid dot? Looks like solid at (−2, 0), then goes down-right to open circle at (4, −4). Also, part of graph is only between x = −2 and x = 4. So:
- Domain: [−2, 4)
- y goes from 0 down to −4 (open at −4), so Range: (−4, 0] ? Wait — lowest y is approaching −4, not reaching; highest is 0 (included). So Range: (−4, 0]

But check: at x = −2, y = 0 (solid). As x increases, y decreases to −4 at x = 4 (open). So yes: Range = (−4, 0]

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4) Horizontal line segment: from x = −2 to x = 5, at y = 5. Both ends solid dots.
- Domain: [−2, 5]
- Range: just y = 5 → {5} or [5, 5] → usually written as {5} or simply 5, but in interval notation: [5, 5]

In most worksheets, they accept “5” or “[5,5]”. We’ll use [5, 5].

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5) Curve: looks like part of a hyperbola or rational function. Starts at bottom left (arrow going down-left), goes up, passes through (−6, −10)? Wait — better: There's a vertical asymptote near x = −2? Actually, graph shows: left branch goes from bottom (−∞, −∞?) up to near x = −2 from left, y → ∞? No — look: At x = −6, y ≈ −10 (solid dot), then curve rises to near x = −2, y → +∞ (arrow up), and right branch starts from near x = −2+, y → −∞, rises to point at (6, 10) (solid dot). So:
- Domain: all x except x = −2 → (−∞, −2) ∪ (−2, ∞)
- Range: all y except maybe a gap? From left branch: y goes from −10 up to ∞; right branch: y from −∞ up to 10. So combined, y takes all real values → (−∞, ∞)

But check endpoints: left end has solid dot at (−6, −10), so y ≥ −10 on left branch? Wait — no, the arrow on left side goes down-left, meaning as x → −∞, y → −∞. So left branch covers (−∞, ∞) except maybe near asymptote. Since it goes to −∞ and +∞ (near x = −2⁻), and right branch goes from −∞ (near x = −2⁺) up to y = 10 (solid), so overall y covers all reals. Yes: Range = (−∞, ∞)

Domain = (−∞, −2) ∪ (−2, ∞)

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6) Parabola opening upward, vertex at (−4, −4) (solid), and goes through (−8, 0) and (0, 0) — symmetric. Arrows up on both ends → extends infinitely up.
- Domain: all real x → (−∞, ∞)
- Range: lowest y is −4 (vertex, solid), then goes up forever → [−4, ∞)

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7) Downward-opening parabola, vertex at (−4, 20) (solid), crosses x-axis near x = −10 and x = 2 (both solid dots). So:
- Domain: from x = −10 to x = 2, inclusive → [−10, 2]
- Range: highest y = 20 (vertex), lowest y = 0 (at endpoints) → [0, 20]

Wait — endpoints are on x-axis, y = 0, solid. So yes, y goes from 0 up to 20. So Range: [0, 20]

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8) Straight line with arrowheads both ends → infinite line.
- Domain: (−∞, ∞)
- Range: (−∞, ∞)

Check: passes through (−4, 4) and (4, −4), slope negative, arrows both ways → yes.

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9) Upward-opening parabola, vertex at (2, −4) (solid), arms go up infinitely. So:
- Domain: all real x → (−∞, ∞)
- Range: y ≥ −4 → [−4, ∞)

Now let’s compile final answers clearly:

1) Domain: [−10, −2) ; Range: [3, 15)
2) Domain: (−∞, ∞) ; Range: (−∞, ∞)
3) Domain: [−2, 4) ; Range: (−4, 0]
4) Domain: [−2, 5] ; Range: [5, 5] (or {5})
5) Domain: (−∞, −2) ∪ (−2, ∞) ; Range: (−∞, ∞)
6) Domain: (−∞, ∞) ; Range: [−4, ∞)
7) Domain: [−10, 2] ; Range: [0, 20]
8) Domain: (−∞, ∞) ; Range: (−∞, ∞)
9) Domain: (−∞, ∞) ; Range: [−4, ∞)

Let me verify #3 again: Graph shows point at (−2, 0) solid, then curve decreasing to (4, −4) open. So x from −2 (included) to 4 (excluded). y from 0 (included) down to −4 (excluded) → so y ∈ (−4, 0]. Yes.

#4: horizontal segment at y=5 from x=−2 to x=5, both ends solid → correct.

#5: tricky. Left part: starts at (−6, −10) solid, then goes up toward vertical asymptote at x = −2, y → ∞. Right part: comes from y → −∞ just right of x = −2, goes up to (6, 10) solid. So y covers (−∞, ∞) — yes, because left side gives y ≥ −10 up to ∞, right side gives y from −∞ up to 10, together all reals.

All good.

Final Answer:
1) Domain: [−10, −2), Range: [3, 15)
2) Domain: (−∞, ∞), Range: (−∞, ∞)
3) Domain: [−2, 4), Range: (−4, 0]
4) Domain: [−2, 5], Range: [5, 5]
5) Domain: (−∞, −2) ∪ (−2, ∞), Range: (−∞, ∞)
6) Domain: (−∞, ∞), Range: [−4, ∞)
7) Domain: [−10, 2], Range: [0, 20]
8) Domain: (−∞, ∞), Range: (−∞, ∞)
9) Domain: (−∞, ∞), Range: [−4, ∞)