Solved Function Notation and Evaluating Functions Pracfice | Chegg.com - Free Printable

Let’s go step by step through each problem on the worksheet.

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Problem 1:
We see a graph with discrete points (dots) plotted on a coordinate plane. To check if it’s a function, we use the vertical line test: if any vertical line hits more than one point, it’s NOT a function.

Looking at the dots:
- At x = -2, there are two y-values: y = 1 and y = -1 → FAILS vertical line test.
→ So, this is a relation, not a function.

But wait — let’s double-check. Actually, looking again: maybe I misread. Let me list the points:

From the graph (approximate):
(-2, 1), (-2, -1), (0, 1), (0, -1), (2, 1), (2, -1)

Yes — multiple y-values for same x → Not a function.

Domain: all x-values present → {-2, 0, 2}
Range: all y-values present → {-1, 1}

But since it’s not a function, we don’t need to give domain/range per instructions? Wait — instruction says: “If it is a function, give the domain and range.” So if not a function, just say “relation”.

✔ Final for #1: Relation

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Problem 2:
Graph shows discrete points again.

Points appear to be:
(-2, 0), (-1, 1), (0, 0), (1, -1), (2, 0)

Check vertical line test: each x has only one y → PASS → It IS a function.

Domain: x-values → {-2, -1, 0, 1, 2}
Range: y-values → {-1, 0, 1}

✔ Final for #2: Function; Domain: {-2, -1, 0, 1, 2}; Range: {-1, 0, 1}

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Problem 3:
This is a V-shaped graph opening to the right — like a sideways absolute value.

It looks like for some x-values (say x=1), there are two y-values (positive and negative). For example, at x=1, y could be 1 or -1.

So vertical line at x=1 would hit two points → FAILS vertical line test.

→ Not a function.

✔ Final for #3: Relation

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Problem 4:
This is a continuous graph — a triangle shape pointing up.

Draw any vertical line — it will intersect the graph at only ONE point. Even at the peak, it’s still one point.

→ Passes vertical line test → It IS a function.

Now find domain and range.

Looking at the graph:
- Leftmost x: -4, rightmost x: 4 → Domain: [-4, 4]
- Lowest y: -2, highest y: 2 → Range: [-2, 2]

✔ Final for #4: Function; Domain: [-4, 4]; Range: [-2, 2]

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Problem 5:
Wave-like curve — sine wave style.

Any vertical line crosses only once → Passes vertical line test → Function.

Domain: from left edge to right edge → looks like x from -4 to 4 → [-4, 4]
Range: lowest y ≈ -2, highest y ≈ 2 → [-2, 2]

✔ Final for #5: Function; Domain: [-4, 4]; Range: [-2, 2]

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Problem 6:
Graph goes down and then curves upward — looks like a parabola opening upward but shifted.

Vertical line test: any vertical line hits only one point → Function.

Domain: appears to go from x = -3 to x = 3 → [-3, 3]
Range: lowest point is at y = -4, goes up to y = 2 → [-4, 2]

Wait — actually, looking closely: the graph starts at top left, goes down to (0, -4), then up to top right. So yes, domain is all x from -3 to 3, range from -4 to 2.

✔ Final for #6: Function; Domain: [-3, 3]; Range: [-4, 2]

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Problem 7:
Input-output table:

Input: 1 → Output: 7 and -7
Input: 2 → Output: 8 and -8

Each input maps to TWO outputs → Not a function.

✔ Final for #7: Relation

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Problem 8:

Input: 3 → 2
Input: 5 → 4
Input: 7 → 6

Each input has exactly one output → Function.

Domain: {3, 5, 7}
Range: {2, 4, 6}

✔ Final for #8: Function; Domain: {3, 5, 7}; Range: {2, 4, 6}

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Problem 9:

Input: 0 → -6
Input: 2 → -4
Input: 4 → -2
Input: 6 → 0

Each input has one output → Function.

Domain: {0, 2, 4, 6}
Range: {-6, -4, -2, 0}

✔ Final for #9: Function; Domain: {0, 2, 4, 6}; Range: {-6, -4, -2, 0}

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Final Answers:

1. Relation
2. Function; Domain: {-2, -1, 0, 1, 2}; Range: {-1, 0, 1}
3. Relation
4. Function; Domain: [-4, 4]; Range: [-2, 2]
5. Function; Domain: [-4, 4]; Range: [-2, 2]
6. Function; Domain: [-3, 3]; Range: [-4, 2]
7. Relation
8. Function; Domain: {3, 5, 7}; Range: {2, 4, 6}
9. Function; Domain: {0, 2, 4, 6}; Range: {-6, -4, -2, 0}