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Domain and Range Practice Problems

based on 8 ratings
By — McGraw-Hill Professional
Updated on Oct 4, 2011

Review the following concept if needed: Domain and Range Help

Domain and Range Practice Problems

Directions: For Problems 2–11, give the domain in interval notation.

1. A function consists of the ordered pairs {( h , 5), ( z , 3), ( i , 12)}. List the elements in the domain.

Introduction to Functions Practice

Solutions

  1. The domain consists of the first coordinate of the ordered pairs— h, z , and i .
  2. We cannot let x − 8 = 0, so we cannot let x = 8. The domain is x ≠ 8, or (−∞, 8) ∪ (8, ∞).
  3. We cannot let x 2 − 2 x = x ( x − 2) = 0, so we cannot let x = 0 or x = 2. The domain is all real numbers except 0 and 2, or (−∞, 0)∪(0, 2)∪(2, ∞).
  4. Because x 2 + 10 = 0 has no real number solution, the domain is all real numbers, or (−∞, ∞).
  5. We can take the cube root of any number, so the domain is all real numbers, or (−∞, ∞).
  6. We must have x + 3 ≥ 0, or x ≥ −3. The domain is [−3, ∞).
  7. We need to solve 4 − x 2 = (2 − x)(2 + x) ≥ 0.

    Introduction to Functions Practice

    Fig. 2.6.

    The domain is [−2, 2].

  8. Because 3 x 2 + 5 ≥ 0 is true for all real numbers, the domain is (−∞, ∞).

  9. We need x − 9 > 0. The domain is x > 9, or (9, ∞).

  10. The domain is all real numbers, or (−∞, ∞).

  11. From x + 5 ≥ 0, we have x ≥ −5.

    Introduction to Functions Practice

    Fig. 2.7

    Now we need to solve x 2 + 2 x − 8 = ( x + 4)(x − 2) = 0.

    x + 4 = 0      x − 2 = 0

    x = −4           x = 2

    Now we need to remove −4 and 2 from x ≥ −5. The domain is [−5, −4)∪(−4, 2) ∪ (2, ∞).

    Introduction to Functions Practice

    Fig. 2.8

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