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 graph appears to be defined from $ x = -10 $ to $ x = 5 $, with no breaks.

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

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6) Graph 6:

- A U-shaped curve, but flipped upside-down? No — actually, it looks like a parabola opening upward, but only the right half?
- Wait: The graph shows a V-shape or absolute value-like shape centered at $ x = -8 $, with vertex at $ (-8, -2) $, and extending to $ x = 0 $, $ y = 2 $.
- But it seems symmetric around $ x = -8 $, going from $ x = -16 $ to $ x = 0 $, with minimum at $ (-8, -2) $, maximum at endpoints $ y = 2 $.

Wait — the graph appears to start at $ x = -16 $, rise to $ (-8, -2) $? No — if it's a U-shape, and minimum is at $ (-8, -2) $, then it opens upward.

But let’s look at the values:
- Left endpoint: $ x = -16 $, $ y = 2 $
- Vertex: $ x = -8 $, $ y = -2 $
- Right endpoint: $ x = 0 $, $ y = 2 $

Yes — this is a parabola opening upward, vertex at $ (-8, -2) $, defined from $ x = -16 $ to $ x = 0 $.

✔ Domain: $ [-16, 0] $
✔ Range: $ [-2, 2] $

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7) Graph 7:

- A parabola opening downward, vertex at $ (-2, 8) $, starting at $ x = -6 $, $ y = 0 $, ending at $ x = 2 $, $ y = 0 $.
- So it's a downward-opening parabola from $ x = -6 $ to $ x = 2 $, with vertex at $ (-2, 8) $.

✔ Domain: $ [-6, 2] $
✔ Range: $ [0, 8] $

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8) Graph 8:

- A line segment from $ x = -5 $ to $ x = 5 $, going from $ (-5, 10) $ to $ (5, -10) $.
- It's a straight line with negative slope.

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

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9) Graph 9:

- A parabola opening upward, vertex at $ (0, -10) $, extending left and right.
- The graph appears to extend from $ x = -10 $ to $ x = 10 $, with $ y $-values from $ -10 $ upward.
- But does it continue forever? No — it's bounded horizontally.
- From $ x = -10 $ to $ x = 10 $, and $ y $ ranges from $ -10 $ to $ 10 $.

Wait — at $ x = 0 $, $ y = -10 $; at $ x = \pm10 $, $ y = 10 $? That would make it symmetric.

So:
- Minimum $ y $: $ -10 $ at $ x = 0 $
- Maximum $ y $: $ 10 $ at $ x = \pm10 $

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

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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) | $[-16, 0]$ | $[-2, 2]$ |
| 7) | $[-6, 2]$ | $[0, 8]$ |
| 8) | $[-5, 5]$ | $[-10, 10]$ |
| 9) | $[-10, 10]$ | $[-10, 10]$ |

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🔍 Explanation Summary:

- Domain = All $ x $-values where the graph exists.
- Range = All $ y $-values the graph reaches.
- Use interval notation for continuous intervals.
- For closed endpoints, use square brackets `[ ]`.
- For open endpoints, use parentheses `( )`, though in these graphs, most are closed.
- For discrete values, like a horizontal line, range can be a single number.

Let me know if you'd like this formatted as a printable answer sheet!