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.
- Looks like part of a cube root function or similar.
- The graph appears to extend leftward and rightward but only shown from $ x = -10 $ to $ x = 10 $, but seems continuous.

Wait — it starts at $ x = -10 $, $ y = -10 $, and goes up to $ x = 10 $, $ y = 10 $. But is it defined for all $ x $? Let's assume it's a continuous increasing curve.

But if it's only drawn from $ x = -10 $ to $ x = 10 $, and has endpoints, then:

- Starts at $ (-10, -10) $, ends at $ (10, 10) $
- Continuously increasing

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

But if it's a function like $ y = x $, then domain and range would be $ (-\infty, \infty) $, but since it's bounded on the graph, we go by what's shown.

Assuming only the segment is drawn, then:

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

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6) Graph 6:

- A parabola-like shape opening upward, vertex at $ (0, -4) $, but only from $ x = -12 $ to $ x = 12 $?
- Wait — it starts at $ x = -12 $, $ y = 0 $, goes down to $ (0, -4) $, then back up to $ x = 12 $, $ y = 0 $.
- So it's a U-shaped curve, symmetric about $ y $-axis, from $ x = -12 $ to $ x = 12 $.

✔ Domain: $ [-12, 12] $
✔ Range: $ [-4, 0] $

Because minimum $ y = -4 $, maximum $ y = 0 $

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7) Graph 7:

- A downward-opening parabola, vertex at $ (-3, 8) $, passing through $ (-1, 0) $ and $ (-5, 0) $.
- It appears to be defined for $ x $ from $ -5 $ to $ -1 $, but wait — does it continue?

Wait — the graph shows a smooth curve starting at $ x = -5 $, going up to $ (-3, 8) $, then down to $ x = -1 $.

So it's a parabola segment from $ x = -5 $ to $ x = -1 $.

✔ Domain: $ [-5, -1] $
✔ Range: $ [0, 8] $

Because the highest point is $ y = 8 $, lowest is $ y = 0 $ at endpoints.

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8) Graph 8:

- A line going from $ (-10, 10) $ to $ (10, -10) $, decreasing.
- It's a straight diagonal line, extending across the grid.

If it's a full line, then:

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

But if only the segment is drawn, check endpoints.

From graph: starts at $ (-10, 10) $, ends at $ (10, -10) $, solid dots.

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

But wait — at $ x = -10 $, $ y = 10 $; at $ x = 10 $, $ y = -10 $, so yes.

So:

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

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9) Graph 9:

- A U-shaped parabola opening upward, vertex at $ (0, -10) $, passing through $ (-10, 0) $ and $ (10, 0) $.
- Symmetric about $ y $-axis.

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

Because minimum $ y = -10 $, maximum $ y = 0 $ at endpoints.

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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) | $[-10, 10]$ | $[-10, 10]$ |
| 6) | $[-12, 12]$ | $[-4, 0]$ |
| 7) | $[-5, -1]$ | $[0, 8]$ |
| 8) | $[-10, 10]$ | $[-10, 10]$ |
| 9) | $[-10, 10]$ | $[-10, 0]$ |

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🔍 Explanation Summary:

- Domain: All $ x $-values where the graph exists.
- Range: All $ y $-values that the graph reaches.
- Use interval notation.
- Closed circles mean included endpoints.
- Open circles mean excluded (but none here).
- For continuous curves, find min/max values and endpoints.

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