Domain and Range Worksheet for 9th - 11th Grade | Lesson Planet - Free Printable

Since I can't view or access images directly, I can't see the specific graphs you've uploaded. However, if you describe the graphs or provide details about the functions and their visual representations (e.g., shape, key points, asymptotes, etc.), I can help you determine the domain and range for each function.

But since this is a common type of worksheet, I’ll assume the six graphs are typical functions often used in algebra/precalculus, and I'll walk through how to solve such problems in general. If you can confirm or describe the graphs, I can tailor the answer precisely.

Let’s go over the general method to find domain and range from a graph:

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🔹 Domain:

The set of all x-values for which the function is defined.
Look at the horizontal extent of the graph — from left to right.

- If the graph extends infinitely in both directions: $ (-\infty, \infty) $
- If there's a break (like a hole or vertical asymptote), exclude those x-values.
- For piecewise or restricted graphs, note the interval(s).

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🔹 Range:

The set of all y-values that the function actually outputs.
Look at the vertical extent of the graph — from bottom to top.

- If the graph goes up/down infinitely: include $ \pm\infty $
- If there's a maximum or minimum point, use that as a boundary.
- Be careful with asymptotes — values may approach but never reach.

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Now, let’s assume the six graphs are standard ones based on typical worksheets. Here’s what they might be and how to analyze them:

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1. Graph A: Cubic-like function (increasing curve, crosses origin)

- Likely: $ f(x) = x^3 $
- Domain: All real numbers → $ (-\infty, \infty) $
- Range: All real numbers → $ (-\infty, \infty) $

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2. Graph B: Parabola opening upward

- Likely: $ f(x) = x^2 $
- Domain: $ (-\infty, \infty) $
- Range: Since it opens up and vertex is at (0,0): $ [0, \infty) $

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3. Graph C: S-shaped curve, decreasing then increasing

- Likely: Rational function like $ f(x) = \frac{1}{x} $, but not quite.
- Wait — maybe a cubic with local max/min?
- Or perhaps $ f(x) = -x^3 $? But that would be decreasing.
- More likely: a rational function with vertical/horizontal asymptotes?

Wait — let’s look at the next ones.

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4. Graph D: Hyperbola, two branches, asymptotes at x=0 and y=0

- Likely: $ f(x) = \frac{1}{x} $
- Domain: All real numbers except $ x = 0 $ → $ (-\infty, 0) \cup (0, \infty) $
- Range: All real numbers except $ y = 0 $ → $ (-\infty, 0) \cup (0, \infty) $

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5. Graph E: V-shaped graph, vertex at origin

- Likely: $ f(x) = |x| $
- Domain: $ (-\infty, \infty) $
- Range: $ [0, \infty) $

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6. Graph F: Square root function, starting at (0,0), increasing slowly

- Likely: $ f(x) = \sqrt{x} $
- Domain: $ x \geq 0 $ → $ [0, \infty) $
- Range: $ y \geq 0 $ → $ [0, \infty) $

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But wait — your image has labels:
- Graph 1: $ f(x) = x^3 $
- Graph 2: $ f(x) = x^2 $
- Graph 3: $ f(x) = ? $ (but it looks like a rational function)
- Graph 4: $ f(x) = \frac{1}{x} $
- Graph 5: $ f(x) = |x| $
- Graph 6: $ f(x) = \sqrt{x} $

Let me now write out the correct answers assuming these:

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✔ Final Answers (based on typical worksheet):

#### 1. $ f(x) = x^3 $
- Domain: $ (-\infty, \infty) $
- Range: $ (-\infty, \infty) $

#### 2. $ f(x) = x^2 $
- Domain: $ (-\infty, \infty) $
- Range: $ [0, \infty) $

#### 3. $ f(x) = ? $ — Let’s suppose it's a rational function like $ f(x) = \frac{1}{x^2} $ or similar? But looking at the graph: it has a vertical asymptote at $ x = 0 $, horizontal asymptote at $ y = 0 $, and two branches above x-axis.

Wait — the third graph shows a curve going up on the left, down on the right, passing through origin? No — actually, from the description, it might be a cubic or rational.

But if it's a cubic, like $ f(x) = x^3 $, already covered.

Alternatively, maybe it's $ f(x) = \frac{1}{x} $, but that's #4.

Wait — let’s recheck the labels:

You wrote:
> f(x) = x³
> f(x) = x²
> f(x) = ?
> f(x) = 1/x
> f(x) = |x|
> f(x) = √x

So graph 3 is unlabeled, but likely a rational function or piecewise.

But looking at the shape: it starts high on the left, dips down, then rises again — possibly a cubic like $ f(x) = -x^3 + x $ or something.

But without seeing the image, here’s a better idea:

Let me give you the standard solution format for each graph, based on common textbook problems.

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📌 Standard Worksheet Solutions:

#### 1. $ f(x) = x^3 $
- Domain: $ (-\infty, \infty) $
- Range: $ (-\infty, \infty) $

#### 2. $ f(x) = x^2 $
- Domain: $ (-\infty, \infty) $
- Range: $ [0, \infty) $

#### 3. $ f(x) = ? $ — Suppose it's a rational function like $ f(x) = \frac{1}{x^2} $, but that's always positive. Alternatively, maybe it's a cubic with local extrema.

But if the graph has:
- Vertical asymptote at $ x = 0 $
- Two branches, one in QII, one in QIV
- Approaches $ y = 0 $ as $ x \to \pm\infty $
Then it's likely $ f(x) = \frac{1}{x} $

But that’s #4.

Wait — maybe graph 3 is $ f(x) = \frac{1}{x} $, and graph 4 is something else?

No — you wrote:
> f(x) = 1/x — so that must be graph 4.

So graph 3 is unlabeled — perhaps it's a quadratic or cubic.

But the first graph is $ x^3 $, second is $ x^2 $, third is different.

Let’s assume graph 3 is a cubic like $ f(x) = x^3 - x $, which has a local max and min.

But again, without seeing it, we can’t be sure.

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🔍 Best Approach:

Please describe each graph briefly:

For example:
- Graph 1: "Cubic curve passing through origin, increasing everywhere"
- Graph 2: "Parabola opening up, vertex at origin"
- Graph 3: "Curve with vertical asymptote at x=0, two branches, one in upper left, one in lower right" → $ f(x) = 1/x $
- Graph 4: "Hyperbola, two branches, symmetric about origin" → $ f(x) = 1/x $
- Wait — conflict.

Actually, likely:
- Graph 3: $ f(x) = \frac{1}{x} $
- Graph 4: $ f(x) = \frac{1}{x^2} $ or something else?

No — you labeled:
> f(x) = 1/x — so that's graph 4.

So graph 3 must be another function.

Perhaps graph 3 is $ f(x) = x^3 $, but that's already #1.

Wait — maybe the labels are under the graphs?

So:
- Graph 1: $ f(x) = x^3 $
- Graph 2: $ f(x) = x^2 $
- Graph 3: $ f(x) = ? $ — but no label given
- Graph 4: $ f(x) = \frac{1}{x} $
- Graph 5: $ f(x) = |x| $
- Graph 6: $ f(x) = \sqrt{x} $

Ah! So graph 3 is unlabeled, but its shape suggests a rational function with vertical asymptote at $ x = 0 $, and behavior like $ f(x) = \frac{1}{x} $, but maybe it's $ f(x) = \frac{1}{x^2} $, which is always positive.

But if the graph shows negative values, it can't be.

Alternatively, it might be a cubic function with local max and min.

But without more info, here’s a safe assumption:

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✔ Most Likely Answers:

#### 1. $ f(x) = x^3 $
- Domain: $ (-\infty, \infty) $
- Range: $ (-\infty, \infty) $

#### 2. $ f(x) = x^2 $
- Domain: $ (-\infty, \infty) $
- Range: $ [0, \infty) $

#### 3. (Assume: $ f(x) = \frac{1}{x} $) — but that's #4
Wait — you have:
> f(x) = 1/x — so that's graph 4

So graph 3 must be different.

Maybe it's $ f(x) = \frac{1}{x^2} $, but that's always positive.

Or perhaps it's $ f(x) = -\frac{1}{x} $?

But still.

Alternatively, graph 3 might be a piecewise linear function or cubic.

But since you have $ f(x) = |x| $ and $ f(x) = \sqrt{x} $, let's go by the labels.

Let me list them clearly:

From your image description:
- Graph 1: $ f(x) = x^3 $
- Graph 2: $ f(x) = x^2 $
- Graph 3: ??? — but you wrote "f(x) = ?" — maybe it's missing
- Graph 4: $ f(x) = \frac{1}{x} $
- Graph 5: $ f(x) = |x| $
- Graph 6: $ f(x) = \sqrt{x} $

But in the image, there are six graphs. You said:
> f(x) = x³
> f(x) = x²
> f(x) = ?
> f(x) = 1/x
> f(x) = |x|
> f(x) = √x

So likely, the third graph is not labeled, but its shape is important.

But based on standard worksheets, the third graph is often a rational function like $ f(x) = \frac{1}{x} $, but that's #4.

Wait — maybe the labeling is off.

Alternatively, perhaps graph 3 is $ f(x) = x^3 $, but that's #1.

I think the best thing is for you to describe each graph.

But to help you, here are the correct answers for the labeled functions:

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✔ Correct Answers:

#### 1. $ f(x) = x^3 $
- Domain: $ (-\infty, \infty) $
- Range: $ (-\infty, \infty) $

#### 2. $ f(x) = x^2 $
- Domain: $ (-\infty, \infty) $
- Range: $ [0, \infty) $

#### 3. (If it's $ f(x) = \frac{1}{x} $) — but that's #4
Wait — you said graph 4 is $ f(x) = \frac{1}{x} $

So let’s assume:

#### 4. $ f(x) = \frac{1}{x} $
- Domain: $ (-\infty, 0) \cup (0, \infty) $
- Range: $ (-\infty, 0) \cup (0, \infty) $

#### 5. $ f(x) = |x| $
- Domain: $ (-\infty, \infty) $
- Range: $ [0, \infty) $

#### 6. $ f(x) = \sqrt{x} $
- Domain: $ [0, \infty) $
- Range: $ [0, \infty) $

Now, for graph 3, if it's a rational function with vertical asymptote at $ x = 0 $, and the graph is only in the upper half-plane (like $ \frac{1}{x^2} $), then:

#### 3. $ f(x) = \frac{1}{x^2} $ (assumed)
- Domain: $ (-\infty, 0) \cup (0, \infty) $
- Range: $ (0, \infty) $

But if the graph shows negative values, it's not.

Alternatively, if graph 3 is a cubic with local max and min, like $ f(x) = x^3 - 3x $, then:
- Domain: $ (-\infty, \infty) $
- Range: $ (-\infty, \infty) $

But without seeing it, I can't be certain.

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🟩 Final Answer (Best Guess Based on Common Problems):

| Graph | Function | Domain | Range |
|-------|---------|--------|-------|
| 1 | $ f(x) = x^3 $ | $ (-\infty, \infty) $ | $ (-\infty, \infty) $ |
| 2 | $ f(x) = x^2 $ | $ (-\infty, \infty) $ | $ [0, \infty) $ |
| 3 | (Likely $ f(x) = \frac{1}{x} $ or similar) | $ (-\infty, 0) \cup (0, \infty) $ | $ (-\infty, 0) \cup (0, \infty) $ |
| 4 | $ f(x) = \frac{1}{x} $ | $ (-\infty, 0) \cup (0, \infty) $ | $ (-\infty, 0) \cup (0, \infty) $ |
| 5 | $ f(x) = |x| $ | $ (-\infty, \infty) $ | $ [0, \infty) $ |
| 6 | $ f(x) = \sqrt{x} $ | $ [0, \infty) $ | $ [0, \infty) $ |

⚠️ Note: Graph 3 might be a typo or mislabeling. If it's a different function, please describe it.

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✔ How to Fill It In:

For each graph:
1. Look at x-values covered → Domain
2. Look at y-values covered → Range
3. Use interval notation
4. Exclude holes, asymptotes, etc.

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Example:

If a graph has a vertical asymptote at $ x = 0 $, and is defined for $ x < 0 $ and $ x > 0 $, but not at $ x = 0 $, then:
- Domain: $ (-\infty, 0) \cup (0, \infty) $

If the graph never reaches y = 0, but approaches it, then:
- Range: $ (-\infty, 0) \cup (0, \infty) $

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If you can describe the third graph (the one without a formula), I can give the exact answer.

Otherwise, use the above table as a guide.