Interval Notation in Mathematics

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Questions and Answers

What is the primary function of the adrenal glands?

  • Filtration of waste products from the blood
  • Regulation of blood sugar levels
  • Production of antibodies to fight infection
  • Production of hormones that regulate blood pressure, metabolism, and stress response (correct)

What type of tissue is the epidermis primarily composed of?

  • Epithelial tissue (correct)
  • Connective tissue
  • Nervous tissue
  • Muscle tissue

What is the main function of the dermis?

  • Production of new skin cells
  • Providing structural support and containing blood vessels, nerves, and glands (correct)
  • Absorption of nutrients and oxygen
  • Protection from UV radiation

What is the function of melanocytes in the skin?

<p>Production of melanin, a pigment that protects against UV radiation (D)</p> Signup and view all the answers

What type of cells are found in the subcutaneous layer?

<p>Adipocytes (C)</p> Signup and view all the answers

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Study Notes

Interval Notation

  • Interval notation uses parentheses and brackets to represent a set of real numbers
  • Parentheses indicate an endpoint is not included
  • Brackets indicate an endpoint is included
  • Infinity symbols are always paired with parentheses

Types of Intervals

  • Open interval: (a, b) represents all values between a and b, but not including a or b. {x | a < x < b}
  • Closed interval: [a, b] represents all values between a and b, including a and b. {x | a ≤ x ≤ b}
  • Half-open (or half-closed) interval: [a, b) represents all values between a and b, including a but not b. {x | a ≤ x < b} or (a, b] represents all values between a and b, including b but not a. {x | a < x ≤ b}
  • Disjoint interval: (-∞, a) ∪ (b, ∞) represents all values less than a or greater than b. {x | x < a or x > b}
  • Infinite interval: (-∞, a) represents all real numbers less than a, (-∞, a] represents all real numbers less than or equal to a, (a, ∞) represents all real numbers greater than a, [a, ∞) represents all real numbers greater than or equal to a;
  • All real numbers: (-∞, ∞) represents the set of all real numbers. {x| x is a real number}

Solving Linear Inequalities

  • Distributive Property: Use the distributive property to clear parentheses.
  • Clear fractions/decimals: Multiply each side of the inequality by a common denominator to eliminate fractions.
  • Combine like terms: Combine all the like terms on each side of the equation.
  • Isolate variable terms: Use the addition property of inequality to get all variable terms on one side.
  • Isolate the variable: Use the multiplication property of inequality to solve for the variable.
  • Reverse inequality: When multiplying or dividing both sides of an inequality by a negative number, flip the inequality sign.

Solving Compound Inequalities

  • "And" Compound Inequalities: Solve each inequality separately, then find the intersection of the solution sets to determine the values that satisfy both inequalities.
  • "Or" Compound Inequalities: Solve each inequality separately, then find the union of the solution sets to determine the values that satisfy at least one of the inequalities.

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