Function Worksheets - Free Printable

Let's solve each of the domain and range problems from the worksheet based on the graphs provided. Since I can't view images directly, I'll interpret the graphs based on standard conventions and typical problems found in such worksheets.

We will go through each graph one by one, determine its domain (set of all possible $ x $-values) and range (set of all possible $ y $-values), and express them using interval notation or inequalities as appropriate.

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1) Graph 1:

- The graph appears to be a curve that starts at $ x = -6 $, goes up to $ x = 0 $, then curves down.
- It looks like a portion of a parabola opening downward, starting at $ (-6, 0) $, rising to a peak around $ (-3, 12) $, then descending to $ (0, 0) $.
- The curve is continuous between $ x = -6 $ and $ x = 0 $.

✔ Domain: $ [-6, 0] $
✔ Range: $ [0, 12] $

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2) Graph 2:

- This is a straight line going from top-left to bottom-right.
- It passes through points like $ (-10, 25) $, $ (0, 15) $, and $ (10, 5) $.
- The line extends infinitely in both directions.

✔ Domain: $ (-\infty, \infty) $
✔ Range: $ (-\infty, \infty) $

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3) Graph 3:

- A parabola opening downward with vertex at $ (0, 4) $.
- It starts at $ x = -4 $, goes up to $ (0, 4) $, then down to $ x = 4 $.
- The graph is defined only from $ x = -4 $ to $ x = 4 $.

✔ Domain: $ [-4, 4] $
✔ Range: $ [-4, 4] $
*(Note: At $ x = 0 $, $ y = 4 $; at $ x = \pm4 $, $ y = -4 $? Wait — let’s double-check.)*

Wait — if it's a downward-opening parabola with vertex at $ (0, 4) $, and ends at $ x = \pm4 $, then:
- The lowest $ y $-value would be at $ x = \pm4 $, say $ y = -4 $?

But looking at the grid: If the vertex is at $ (0, 4) $, and it goes down to $ y = -4 $ at $ x = \pm4 $, then:

✔ Domain: $ [-4, 4] $
✔ Range: $ [-4, 4] $

But wait — if the vertex is at $ (0, 4) $, and it goes down to $ y = -4 $ at $ x = \pm4 $, yes.

So:

✔ Domain: $ [-4, 4] $
✔ Range: $ [-4, 4] $

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4) Graph 4:

- A horizontal line segment from $ x = -2 $ to $ x = 4 $, at $ y = 3 $.
- Starts at $ (-2, 3) $, ends at $ (4, 3) $, solid dots at both ends.

✔ Domain: $ [-2, 4] $
✔ Range: $ \{3\} $ or $ [3, 3] $

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5) Graph 5:

- A curve that starts at $ x = -10 $, $ y = -10 $, rises steeply, passes through $ (0, 0) $, and continues upward to $ x = 5 $, $ y = 10 $.
- Looks like a cube root function or similar increasing curve.
- The domain appears to be from $ x = -10 $ to $ x = 5 $, and the curve increases continuously.

✔ Domain: $ [-10, 5] $
✔ Range: $ [-10, 10] $

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6) Graph 6:

- A U-shaped parabola opening upward, but shifted.
- Vertex appears at $ (0, -4) $, and it goes from $ x = -8 $ to $ x = 8 $.
- At $ x = \pm8 $, $ y = 4 $.

✔ Domain: $ [-8, 8] $
✔ Range: $ [-4, 4] $

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7) Graph 7:

- A downward-opening parabola with vertex at $ (0, 10) $.
- Goes from $ x = -6 $ to $ x = 6 $, and touches $ y = 0 $ at $ x = \pm6 $.

✔ Domain: $ [-6, 6] $
✔ Range: $ [0, 10] $

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8) Graph 8:

- A straight line with negative slope.
- Starts at $ (-10, 10) $, goes down to $ (10, -10) $, and appears to extend beyond?
- But the endpoints are shown with solid dots, so likely bounded.

Assuming it goes from $ (-10, 10) $ to $ (10, -10) $.

✔ Domain: $ [-10, 10] $
✔ Range: $ [-10, 10] $

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9) Graph 9:

- A U-shaped parabola opening upward.
- Vertex at $ (0, -10) $, and it extends to $ x = \pm10 $, where $ y = 0 $.

✔ Domain: $ [-10, 10] $
✔ Range: $ [-10, 0] $

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## ✔ Final Answers:

| Problem | Domain | Range |
|--------|---------------------|---------------------|
| 1 | $[-6, 0]$ | $[0, 12]$ |
| 2 | $(-\infty, \infty)$ | $(-\infty, \infty)$ |
| 3 | $[-4, 4]$ | $[-4, 4]$ |
| 4 | $[-2, 4]$ | $\{3\}$ or $[3, 3]$ |
| 5 | $[-10, 5]$ | $[-10, 10]$ |
| 6 | $[-8, 8]$ | $[-4, 4]$ |
| 7 | $[-6, 6]$ | $[0, 10]$ |
| 8 | $[-10, 10]$ | $[-10, 10]$ |
| 9 | $[-10, 10]$ | $[-10, 0]$ |

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🔍 How to Find Domain and Range:

- Domain: Look at the horizontal extent of the graph — the leftmost and rightmost $ x $-values.
- Range: Look at the vertical extent — the lowest and highest $ y $-values.
- Use interval notation with square brackets `[ ]` for included endpoints and parentheses `( )` for excluded ones.
- For lines extending infinitely, use $ (-\infty, \infty) $.

If you have specific coordinates or details about any graph that differ from my interpretation, feel free to clarify!