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Domain and Range Worksheet

Find allowable inputs and attainable outputs, including discrete contexts. Includes a worked example, printable practice, and an answer key with explanations.

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Grade 11 Math Functions OperationsDomain and Range

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Includes

2 Text2 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.A.1CCSS.MATH.CONTENT.HSF.IF.B.5

Topics

mathfunctionsdomainrangegrade 11
9 sections · Free to use · Printable
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Domain and Range Review

Name:

Date:

Score:

Learning goal and worked example

Find allowable inputs and attainable outputs, including discrete contexts.

For y = √(x−2)+3, require x−2 ≥ 0: domain [2,∞). Since √(x−2) ≥ 0, range [3,∞).

Distinguish the whole function from the graph window. Counts such as shirts are integers, not a continuous interval.

Read each question carefully and determine the domain and range for the given functions or scenarios. Express your answers using interval notation where appropriate.

1. The graph shows y = x² - 1. The parabola continues beyond the viewing window. Determine its domain and range.

y = x² - 1 (continues beyond the window)-5-5-4-4-3-3-2-2-1-1001122334455y = x² - 1 (continues beyond the window)xy

Domain:  

Range:  

2. Which of the following functions has a domain restriction of x ≠ 3?

a

f(x) = √(x + 3)

b

g(x) = 1 / (x - 3)

c

h(x) = x² + 3

d

k(x) = |x - 3|

3. For the function f(x) = √(x - 4):

The domain is  .

The range is  .

4. For the function g(x) = 2 / (x + 1):

The domain is  .

The range is  .

5. A company manufactures custom t-shirts. The cost C (in dollars) to produce 'x' t-shirts is given by the function C(x) = 50 + 8x. If the company can produce a maximum of 500 t-shirts per day, determine the practical domain and range for this function.

Practical Domain:  

Practical Range:  

6. The domain of any polynomial function is all real numbers.

T

True

F

False

7. For a function f(x) = |x|, the range is all real numbers.

T

True

F

False

Answer key and worked solutions

1. For y=x²−1: domain (−∞,∞), range [−1,∞). The graph window does not restrict the parabola.

2. b, g(x)=1/(x−3).

3. x−4≥0, so domain [4,∞); the square root is nonnegative, so range [0,∞).

4. Domain (−∞,−1) ∪ (−1,∞); range (−∞,0) ∪ (0,∞). The numerator 2 prevents an output of zero.

5. Practical domain {0,1,2,…,500} shirts. Practical range {50+8n : n=0,1,…,500} dollars = {50,58,66,…,4050}. Only these discrete values occur, not every real number between the endpoints.

6. True for a polynomial with its natural real domain. 7. False: |x| has range [0,∞).

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