Question 1

Which region in the Venn diagram represents the intersection $$A \cap B of $$sets $$A$$ and $$B$$?

Accepted Answer

The region that is in both set $$A$$ and set $$B.$$

Question 2

Solve the compound inequality $$-2 \u003c x$$ and $$x \leq 0. $$Write the solution in interval notation.

Accepted Answer

$$(-2, 0]$$

Question 3

Which of the following best describes a conjunction in mathematics?

Accepted Answer

A statement joined by the word 'and', representing the intersection of solution sets.

Question 4

Solve and graph: $$3 \leq 2x - 1 \u003c 7. $$What is the solution in set-builder notation?

Accepted Answer

$$\{x \mid 2 \leq x \u003c 4\}$$

Question 5

Which of the following is the union of the sets $$\{a, b, c, d, e\}$$ and $$\{d, e, f, g\}$$?

Accepted Answer

$$\{a, b, c, d, e, f, g\}$$

Question 6

Solve and graph: $$x \u003c -4 or$$ $$x \geq 2. $$What is the solution in interval notation?

Accepted Answer

$$(-\infty, -4) \cup [2, \infty)$$

Question 7

Find the domain of the function $$f(x) = \frac{2x+1}{x-3} in $$interval notation.

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 8

Which of the following is the correct interval notation for the solution to $$2x - 3 \u003e 1$$ and $$3x - 1 \u003c 2$$?

Accepted Answer

$$(1, 2)$$

Question 9

A function $$f(x) = \sqrt{8 - 2x} is $$defined for which values of $$x$$?

Accepted Answer

$$x \leq 4$$

Question 10

Solve and graph: $$-5x + 3 \leq 13$$ and $$4x - 5 \leq 7. $$What is the solution in interval notation?

Accepted Answer

$$[-2, 3]$$

Question 11

Which of the following best describes a disjunction in mathematics?

Accepted Answer

A statement joined by the word 'or', representing the union of solution sets.

Question 12

Find the domain of $$f(x) = \sqrt{3 - x} in $$set-builder notation.

Accepted Answer

$$\{x \mid x \leq 3\}$$

Question 13

Solve and graph: $$2x + 1 \geq 3 or$$ $$4x \u003c -4. $$What is the solution in interval notation?

Accepted Answer

$$[1, \infty) \cup (-\infty, -1)$$

Question 14

Which of the following is the correct set-builder notation for the solution to $$x  0$$?

Accepted Answer

$$\{x \mid x  0\}$$

Question 15

A real-world scenario: A medication is safe to use if the patient's temperature $$T$$ satisfies $$97 \u003c T \u003c 100 (in $$degrees Fahrenheit). Which notation correctly describes the safe temperature range?

Accepted Answer

$$(97, 100)$$

Intersections, Unions, and Compound Inequalities: Study Notes for Intermediate Algebra

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