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Domain & Range of Functions — Easy Worksheet 1
Grade 12 · MathSheets Name: ____________________ Date: __________
Answer each question about the domain or range. When a question asks for excluded values, write them like x = 2 or x = -3.
How to solve
A fraction is undefined where its denominator is 0, so exclude those x-values. A square root needs the inside to be ≥ 0, so solve that inequality. For y = a(x - h)2 + k the range starts at k: y ≥ k when a > 0 and y ≤ k when a < 0.
Example
Which x-value is excluded from the domain of f(x) = 3x + 4x - 1?
Answer: x = 1
Not quite. The answer is
💡 A fraction is undefined when its denominator is 0. Set x − 1 = 0: x = 1 is excluded. The answer is x = 1.
✓ Correct!
Not quite. The answer is
💡 A fraction is undefined when its denominator is 0. Set x − 1 = 0: x = 1 is excluded. The answer is x = 1.
💡 How to solve: Domain & Range of Functions
A fraction is undefined where its denominator is 0, so exclude those x-values. A square root needs the inside to be ≥ 0, so solve that inequality. For y = a(x - h)2 + k the range starts at k: y ≥ k when a > 0 and y ≤ k when a < 0.
Try a similar one
Which x-value is excluded from the domain of f(x) = 9x - 2?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The expression under a square root must be ≥ 0: x + 1 ≥ 0. Subtract 1 from both sides: x ≥ −1. So x ≥ −1 and k = −1.
✓ Correct!
Not quite. The answer is
💡 The expression under a square root must be ≥ 0: x + 1 ≥ 0. Subtract 1 from both sides: x ≥ −1. So x ≥ −1 and k = −1.
💡 How to solve: Domain & Range of Functions
A fraction is undefined where its denominator is 0, so exclude those x-values. A square root needs the inside to be ≥ 0, so solve that inequality. For y = a(x - h)2 + k the range starts at k: y ≥ k when a > 0 and y ≤ k when a < 0.
Try a similar one
Which x-value is excluded from the domain of f(x) = 5x - 1?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 This is vertex form a(x − h)2 + k with vertex (−1, −4). a = 2 > 0, so the parabola opens up and its lowest y-value is the vertex's y: y ≥ −4. So k = −4.
✓ Correct!
Not quite. The answer is
💡 This is vertex form a(x − h)2 + k with vertex (−1, −4). a = 2 > 0, so the parabola opens up and its lowest y-value is the vertex's y: y ≥ −4. So k = −4.
💡 How to solve: Domain & Range of Functions
A fraction is undefined where its denominator is 0, so exclude those x-values. A square root needs the inside to be ≥ 0, so solve that inequality. For y = a(x - h)2 + k the range starts at k: y ≥ k when a > 0 and y ≤ k when a < 0.
Try a similar one
Which x-value is excluded from the domain of f(x) = 3x + 7x - 3?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The endpoints are (−4, −6) and (6, 3). The range is the y-values the segment covers: from −6 to 3. So the largest value is 3.
✓ Correct!
Not quite. The answer is
💡 The endpoints are (−4, −6) and (6, 3). The range is the y-values the segment covers: from −6 to 3. So the largest value is 3.
💡 How to solve: Domain & Range of Functions
A fraction is undefined where its denominator is 0, so exclude those x-values. A square root needs the inside to be ≥ 0, so solve that inequality. For y = a(x - h)2 + k the range starts at k: y ≥ k when a > 0 and y ≤ k when a < 0.
Try a similar one
Which x-value is excluded from the domain of f(x) = 2x + 2x + 2?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A fraction is undefined when its denominator is 0. The denominator is x, so x = 0 is excluded. The answer is x = 0.
✓ Correct!
Not quite. The answer is
💡 A fraction is undefined when its denominator is 0. The denominator is x, so x = 0 is excluded. The answer is x = 0.
💡 How to solve: Domain & Range of Functions
A fraction is undefined where its denominator is 0, so exclude those x-values. A square root needs the inside to be ≥ 0, so solve that inequality. For y = a(x - h)2 + k the range starts at k: y ≥ k when a > 0 and y ≤ k when a < 0.
Try a similar one
Which x-value is excluded from the domain of f(x) = 6x + 4?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The expression under a square root must be ≥ 0: x + 2 ≥ 0. Subtract 2 from both sides: x ≥ −2. So x ≥ −2 and k = −2.
✓ Correct!
Not quite. The answer is
💡 The expression under a square root must be ≥ 0: x + 2 ≥ 0. Subtract 2 from both sides: x ≥ −2. So x ≥ −2 and k = −2.
💡 How to solve: Domain & Range of Functions
A fraction is undefined where its denominator is 0, so exclude those x-values. A square root needs the inside to be ≥ 0, so solve that inequality. For y = a(x - h)2 + k the range starts at k: y ≥ k when a > 0 and y ≤ k when a < 0.
Try a similar one
Which x-value is excluded from the domain of f(x) = 2x - 2?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 This is vertex form a(x − h)2 + k with vertex (−3, 3). a = 2 > 0, so the parabola opens up and its lowest y-value is the vertex's y: y ≥ 3. So k = 3.
✓ Correct!
Not quite. The answer is
💡 This is vertex form a(x − h)2 + k with vertex (−3, 3). a = 2 > 0, so the parabola opens up and its lowest y-value is the vertex's y: y ≥ 3. So k = 3.
💡 How to solve: Domain & Range of Functions
A fraction is undefined where its denominator is 0, so exclude those x-values. A square root needs the inside to be ≥ 0, so solve that inequality. For y = a(x - h)2 + k the range starts at k: y ≥ k when a > 0 and y ≤ k when a < 0.
Try a similar one
Which x-value is excluded from the domain of f(x) = 5x - 3?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The endpoints are (−1, 6) and (4, −5). The range is the y-values the segment covers: from −5 to 6. So the smallest value is −5.
✓ Correct!
Not quite. The answer is
💡 The endpoints are (−1, 6) and (4, −5). The range is the y-values the segment covers: from −5 to 6. So the smallest value is −5.
💡 How to solve: Domain & Range of Functions
A fraction is undefined where its denominator is 0, so exclude those x-values. A square root needs the inside to be ≥ 0, so solve that inequality. For y = a(x - h)2 + k the range starts at k: y ≥ k when a > 0 and y ≤ k when a < 0.
Try a similar one
Which x-value is excluded from the domain of f(x) = 1x - 4?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Domain & Range of Functions — Easy Worksheet 1
Answer each question about the domain or range. When a question asks for excluded values, write them like x = 2 or x = -3.