Skills · Functions · Function Fundamentals

Domain and range from a rule

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

• the domain of a square root: y = √(x − 3): domain
• the range of x² plus a number: y = x² + 2: range
• a line: all real numbers: y = 2x − 1: domain
• the range of a parabola that opens down: y = −(x − 1)² + 4: range
• the range of a shifted square root: y = √(x + 2) − 1: range

Sample Sheet · Level 1

1. y = √x − 4: domain =
2. y = √x + 5: domain =
3. y = √x − 5: domain =
4. y = √x + 7: domain =
5. y = x² − 6: range =
6. y = x² − 1: range =
7. y = x² − 3: range =
8. y = x² − 8: range =

Answer key

1. x ≥ 4
2. x ≥ −5
3. x ≥ 5
4. x ≥ −7
5. y ≥ −6
6. y ≥ −1
7. y ≥ −3
8. y ≥ −8

Sample Sheet · Level 3

1. y = √x + 5: domain =
2. y = √x − 5: domain =
3. y = −3x + 8: domain =
4. y = √x − 5 − 3: range =
5. y = x² − 4: range =
6. y = x² + 8: range =
7. y = −(x + 2)² − 5: range =
8. y = −(x − 1)² − 8: range =

Answer key

1. x ≥ −5
2. x ≥ 5
3. all real numbers
4. y ≥ −3
5. y ≥ −4
6. y ≥ 8
7. y ≤ −5
8. y ≤ −8

Make your own

Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.

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