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Chapter 1 Introduction to Functions and Graphs

Chapter 1 Introduction to Functions and Graphs. Numbers, Data and Problem Solving. 1.1. Recognize common sets of numbers Evaluate Expressions by applying the order of operations Learn scientific notation and use it in applications Apply problem solving strategies.

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Chapter 1 Introduction to Functions and Graphs

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  1. Chapter 1 Introduction to Functions and Graphs

  2. Numbers, Data and Problem Solving 1.1 Recognize common sets of numbers Evaluate Expressions by applying the order of operations Learn scientific notation and use it in applications Apply problem solving strategies

  3. Natural Numbers and Integers Natural Numbers (or counting numbers) are numbers in the set N = {1, 2, 3, ...}. Integers are numbers in the set I = {… 3, 2, 1, 0, 1, 2, 3, ...}.These are the natural numbers, their additive inverses (negatives), and 0.

  4. Rational Numbers Rational Numbers are numbers which can be expressed as the ratio of two integers p/q where q 0 Examples: Note that: • Every integer is a rational number. • Rational numbers can be expressed as decimals that either terminate (end) or repeat a sequence of digits.

  5. Irrational Numbers Irrational Numbers are numbers which are not rational numbers. Irrational numbers: • Cannot be expressed as the ratio of two integers. • Have a decimal representation which does not terminate and does not repeat a sequence of digits. Examples:

  6. Real Numbers Real Numbers are can be represented by decimal numbers. Real numbers include both the rational and irrational numbers.Examples:

  7. : rational number Example: Classify Numbers Classify each number as one or more of the following: natural number, integer, rational number, irrational number. Solution 5: natural number, integer, rational number –1.2: rational number

  8. : irrational number : natural number, integer, rational number Example: Classify Numbers Solution (continued) –12: integer, rational number

  9. Order of Operations Using the following order of operations, first perform all calculations within parentheses, square roots, and absolute value bars and above and below fraction bars. Then use the same order of operations to perform any remaining calculations. • 1. Evaluate all exponents. Then do any negation after evaluating exponents. • 2. Do all multiplication and division from left to right. • 3. Do all addition and subtraction from left to right.

  10. Example: Evaluating Arithmetic Expressions Evaluate each expression by hand. Solution

  11. Scientific Notation A real number r is in scientific notation when r is written as c 10n, where 1 ≤ |c| < 10 and n is an integer. Examples: • The distance to the sun is 93,000,000 mi. • In scientific notation this is 9.3  107 mi. • The size of a typical virus is 0.000005 cm. • In scientific notation this is 5  106 cm.

  12. Example: Evaluating Expressions by Hand Evaluate each expression. Write your result in scientific notation and standard form.

  13. Example: Evaluating Expressions by Hand Solution

  14. Example: Evaluating Expressions by Hand Solution (continued)

  15. Problem Solving • Possible Solution Strategies • Make a sketch. • Apply formulas.

  16. Example: Finding the Volume of a soda can The volume V of the cylindrical soda can is given by V = r2h, where r is its radius and h is its height. a. If r = 1.4 inches and h = 5 inches, find the volume of the can in cubic inches. b. Could this can hold 16 fluid ounces? (Hint: 1 cubic inch equals 0.55 fluid ounces.) Solution

  17. Example: Finding the Volume of a soda can b. Could this can hold 16 fluid ounces? (Hint: 1 cubic inch equals 0.55 fluid ounces.) To find the number of fluid ounces, multiply the number of cubic inches by 0.55. Yes, the can could hold 16 fluid ounces.

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