Or press and hold the picture and choose “Save image”.
for Whoobee's shop
Domain & Range of Functions — Easy Worksheet 2
Grade 12 · Whoobee 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 − 3 = 0: x = 3 is excluded. The answer is x = 3.
✓ Correct!
Not quite. The answer is
💡 A fraction is undefined when its denominator is 0. Set x − 3 = 0: x = 3 is excluded. The answer is x = 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) = 4x?
✓ 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: 2x + 6 ≥ 0. Subtract 6 from both sides: 2x ≥ −6. Divide both sides by 2: x ≥ −3. So x ≥ −3 and k = −3.
✓ Correct!
Not quite. The answer is
💡 The expression under a square root must be ≥ 0: 2x + 6 ≥ 0. Subtract 6 from both sides: 2x ≥ −6. Divide both sides by 2: x ≥ −3. So x ≥ −3 and 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) = 8x - 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, −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 (3, −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) = 2x + 1x - 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 endpoints are (0, −5) and (6, 4). The range is the y-values the segment covers: from −5 to 4. So the largest value is 4.
✓ Correct!
Not quite. The answer is
💡 The endpoints are (0, −5) and (6, 4). The range is the y-values the segment covers: from −5 to 4. So the largest value is 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) = 4x + 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
💡 A fraction is undefined when its denominator is 0. Set x − 5 = 0: x = 5 is excluded. The answer is x = 5.
✓ Correct!
Not quite. The answer is
💡 A fraction is undefined when its denominator is 0. Set x − 5 = 0: x = 5 is excluded. The answer is x = 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) = 4x + 3x - 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
💡 The expression under a square root must be ≥ 0: x − 3 ≥ 0. Add 3 to both sides: x ≥ 3. So x ≥ 3 and k = 3.
✓ Correct!
Not quite. The answer is
💡 The expression under a square root must be ≥ 0: x − 3 ≥ 0. Add 3 to both sides: x ≥ 3. So x ≥ 3 and 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) = 3x + 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 (−1, −3). a = 1 > 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 (−1, −3). a = 1 > 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) = 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 (−6, 4) and (3, −6). The domain is the x-values the segment covers: from −6 to 3. So the largest value is 3.
✓ Correct!
Not quite. The answer is
💡 The endpoints are (−6, 4) and (3, −6). The domain is the x-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) = 5x - 2?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Log in to save your progress.
Domain & Range of Functions — Easy Worksheet 2
Answer each question about the domain or range. When a question asks for excluded values, write them like x = 2 or x = -3.