Domain and Range Review

Domain and Range

By Jason Dunn

D = {-3, -1, 1, 4, 5}​

Order doesn't actually matter, but often you'll see least to greatest.

Domain is the set of all x values

R = {-5, 0, 2, 6}

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Don't repeat the 2​

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Range is the set of y-values

Fill in the Blanks

What is the domain of this chart of values?

*Don't add spaces in between

Domain (x) = {-1, 0, 1, 2, 3}

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Range (y) = {1, 2, 3}​

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"Discrete" Function consists of scattered points​

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Multiple Choice

Which of these sets is the RANGE of the graph?

• A. {0, 6, 12, 18}

• B. {-2, 0, 2, 4}

• C. {-2, 2, 4}

• D. {6, 12, 18}

Multiple Choice

Which number is NOT an element of the domain?

• A. 2

• B. 1

• C. 0

• D. 6

Fill in the Blanks

What is the corresponding element in the domain when the element in the range is 3?

R: {-4 ≤ y ≤ 0} or [-4, 0]

​Graph goes as low as -4 and as high as 0

"Continuous" Graph

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D: {-3 < x ≤ 1} or (-3, 1]

​Graph goes as far left as to the left in -3, and as far right as 1

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Multiple Choice

What is the domain of this graph?

• A. {-2 $$\le$$ x $$\le$$ 4}

• B. {-5 $$\le$$ x $$\le$$ 4}

• C. {-4, 0, -2}

• D. {-4 $$\le$$ x $$\le$$ 2}

Multiple Choice

Which number is outside the domain for this zig-zag shaped graph?

• A. -3

• B. 2

• C. 0

• D. 4

Fill in the Blanks

What is the range of this relation?

*use interval notation

Some graphs go forever in a direction (just one inequality sign)

Multiple Choice

What is the domain of this graph?

(NOTE: Each grid is one unit)

• A. All Real Numbers

• B. x ≥ -2

• C. x $$\le$$ 6

• D. -2 $$\le$$ x $$\le$$ 6

Domain is "all real numbers"

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It looks like it goes full vertical, but it doesn't.

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Range is "everything above 0" so {y ≥ 0}

Consider this

Multiple Choice

What is the range of the given function?

• A. all real numbers

• B. $$y\ge-4$$

• C. $$y\le7$$

• D. $$y\le-4$$

Multiple Choice

What is the range of this graph?

• A. $$y\le3$$

• B. y > -3

• C. $$y\ge0$$

• D. All Real Numbers

Real life Applications

Multiple Choice

A student rode a bike from school to a recreation center. The graph shows the student's distance in miles from the recreation center after riding the bike for x minutes. What is the range of the function for this situation?

• A. All real numbers greater than or equal to zero and less than or equal to 28.

• B. All real numbers greater than or equal to zero and less than or equal to 9.

• C. All real numbers less than or equal to 28.

• D. All real numbers less than or equal to 9.

Multiple Choice

A student worked out at a gym continuously for 5 minutes. The graph shows the remaining percentage of workout as a linear function of x, the time in minutes. Which best describes the domain and range of the function for this situation?

• A.

  Domain: All real numbers greater than or equal to zero and less than or equal to 100.

  Range: All real numbers greater than or equal to zero and less than or equal to 50.

• B.

  Domain: {-2}

  Range: {100}

• C.

  Domain: All real numbers greater than or equal to zero and less than or equal to 50.

  Range: All real numbers greater than or equal to zero and less than or equal to 100.

• D.

  Domain: {100}

  Range: {-2}

Multiple Choice

The total cost (in dollars) to buy uniforms for the players on a volleyball team can be found using the function $$c=34.95u+6.25$$ , where u is the number of uniforms bought. If there are at least 8 players but not more than 12 players on the volleyball team, what is the DOMAIN for the function of this situation?

• A. $$0<u\le12$$

• B. $$0<u\le425.65$$

• C. {8, 9, 10, 11, 12}

• D. {285.85, 320.80, 355.75, 390.70, 425.65}

Multiple Choice

A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plate weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by $$f\left(x\right)=20x+4$$ .

What is the RANGE of the function for this situation?

• A. {0, 1, 2, 3, 4, 5, 6}

• B. {4, 24, 44, 64, 84, 104, 124}

• C. {0, 2, 4, 6}

• D. {4, 44, 84, 124}