Engaging students: Finding the domain and range of a function ... - Free Printable

Since the actual graphs labeled A to L are not visible in your message, I can't directly match the domains, ranges, and function status to specific graph letters. However, I can analyze each problem and describe what kind of graph would match each description. Once you have the graphs (A–L), you can use this analysis to identify the correct letter.

Let’s go through each one step by step:

---

1.

- Domain: $ \{-4 \leq x \leq 4\} $
- Range: $ \{-4 \leq y \leq 4\} $
- Function: NO

✔ This means:
- The graph exists only between $x = -4$ and $x = 4$, inclusive.
- The $y$ values go from $-4$ to $4$, inclusive.
- But it is not a function, so at least one vertical line will intersect the graph at more than one point.

🔍 Possible shape: A non-function like a circle or sideways parabola within that domain and range.

👉 Look for a closed curve (e.g., circle) centered at origin with radius 4, but only over $[-4,4]$ in both directions.

→ Likely Graph: C or G (if they show a circle or oval)

---

2.

- Domain: $ \{-3 < x \leq 5\} $
- Range: $ \{y = -1\} $
- Function: YES

✔ This is a horizontal line at $y = -1$, but:
- $x$ starts just after $-3$ (open circle at $x = -3$)
- Ends at $x = 5$ (closed circle)

So: Horizontal line segment at $y = -1$, from $x = -3$ (not including) to $x = 5$ (including).

→ This is a function because every $x$ has exactly one $y$.

👉 Look for a horizontal line at $y = -1$, starting with an open dot at $x = -3$, ending with closed dot at $x = 5$

→ Likely Graph: F or J

---

3.

- Domain: $ \{-4 \leq x \leq 2\} $
- Range: $ \{-2 \leq y \leq 4\} $
- Function: YES

✔ Graph defined from $x = -4$ to $x = 2$, $y$ from $-2$ to $4$
- It's a function, so passes vertical line test
- Could be a line segment, parabola, etc., but no "double" outputs

→ Look for a graph that:
- Starts at $x = -4$, ends at $x = 2$
- $y$ values between $-2$ and $4$
- No multiple $y$'s for same $x$

→ Possibly a line segment, or increasing curve

→ Likely Graph: B or E

---

4.

- Domain: $ \{x > 0\} $
- Range: $ \{y = 4\} $
- Function: YES

✔ Horizontal line at $y = 4$, but only for $x > 0$
- Open at $x = 0$, goes to infinity rightward

→ Horizontal ray starting at $x = 0$ (open), going right, at height $y = 4$

→ Likely Graph: D or H

---

5.

- Domain: $ \{-6 \leq x \leq 6\} $
- Range: $ \{0 \leq y \leq 6\} $
- Function: YES

✔ Graph from $x = -6$ to $x = 6$, $y$ from $0$ to $6$
- Must pass vertical line test
- Could be a semicircle, V-shape, or parabola opening up

But since range starts at 0, maybe bottom of a U-shaped curve

→ Likely Graph: A or K

---

6.

- Domain: $ \{x = -5\} $
- Range: $ \{-2 < y < 6\} $
- Function: NO

✔ Only defined at $x = -5$, but $y$ varies from $-2$ to $6$, not including endpoints
- So it's a vertical line segment at $x = -5$, from $y = -2$ to $y = 6$, open at both ends

But: Not a function — because one $x$ ($-5$) maps to many $y$ values → violates definition of function

→ Look for a vertical line segment at $x = -5$, open at both ends

→ Likely Graph: I or L

---

7.

- Domain: $ \{x \geq 0\} $
- Range: $ \{\text{all real numbers}\} $
- Function: NO

✔ Defined for all $x \geq 0$, but $y$ covers all real numbers
- Not a function → must fail vertical line test somewhere
- Could be a sideways parabola or circle extending to the right

For example: $x = y^2$, which opens to the right

→ At $x = 1$, $y = \pm1$: two outputs → not a function

→ Look for a right-opening parabola starting at $x = 0$, going to infinity

→ Likely Graph: M? Wait — only A–L. Maybe Graph: H or J?

Wait — let’s check: if it’s $x = y^2$, then domain $x \geq 0$, range all real $y$. Yes.

→ Likely Graph: H or J, depending on how it's drawn

---

8.

- Domain: $ \{-3 \leq x \leq 4\} $
- Range: $ \{-2 \leq y \leq 4\} $
- Function: NO

✔ Defined from $x = -3$ to $x = 4$, $y$ from $-2$ to $4$
- But not a function, so some $x$ has multiple $y$ values

→ Could be a circle, ellipse, or sideways U

→ Look for a closed curve (like a circle) within those bounds

→ Likely Graph: C or G

---

9.

- Domain: $ \{\text{all real numbers}\} $
- Range: $ \{\text{all real numbers}\} $
- Function: YES

✔ Graph defined everywhere, outputs all real numbers
- And it is a function

→ Examples: linear function like $y = x$, or cubic, etc.

→ Look for a continuous curve that extends infinitely left/right and up/down, passing vertical line test

→ Likely Graph: A or K (if it's a line or cubic)

---

Now, here's a summary table with likely matches based on typical graph types:

| # | Description | Likely Graph |
|---|-------------|--------------|
| 1 | Domain [-4,4], Range [-4,4], NOT function | C or G (circle) |
| 2 | Domain (-3,5], Range {y=-1}, Function YES | F or J (horizontal line segment) |
| 3 | Domain [-4,2], Range [-2,4], Function YES | B or E (curve or line) |
| 4 | Domain x>0, Range {y=4}, Function YES | D or H (horizontal ray) |
| 5 | Domain [-6,6], Range [0,6], Function YES | A or K (U-shaped or semicircle) |
| 6 | Domain {x=-5}, Range (-2,6), NOT function | I or L (vertical segment) |
| 7 | Domain x≥0, Range all reals, NOT function | H or J (sideways parabola) |
| 8 | Domain [-3,4], Range [-2,4], NOT function | C or G (closed curve) |
| 9 | Domain all reals, Range all reals, Function YES | A or K (linear or cubic) |

---

⚠️ Since you mentioned “attached page” with graphs A–L, you’ll need to compare these descriptions to the actual images.

But here’s how to match them correctly:

Tips for matching:

- Function vs. Not: Use Vertical Line Test
- If any vertical line crosses graph more than once → NOT a function
- Domain: look at leftmost to rightmost x-values
- Range: look at bottom to top y-values

---

Final Answer Format (you fill in):

```
___ 1. ___ 2. ___ 3.
___ 4. ___ 5. ___ 6.
___ 7. ___ 8. ___ 9.
```

Once you have the graphs, apply the above logic.

If you can describe or upload the graphs A–L, I can help you match them exactly.