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5–Minute Check 1

Find the value of x 2 + 4 x + 4 if x = –2. A. –8 B. 0 C. 4 D. 16. 5–Minute Check 1. Evaluate | x – 2 y | – |2 x – y | – xy if x = –2 and y = 7. A. –9 B. 9 C. 19 D. 41. 5–Minute Check 3. Factor 8 xy 2 – 4 xy. A. 2 x (4 xy 2 – y ) B. 4 xy (2 y – 1) C. 4 xy ( y 2 – 1)

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5–Minute Check 1

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  1. Find the value of x2 + 4x + 4 if x = –2. A.–8 B.0 C.4 D.16 5–Minute Check 1

  2. Evaluate |x – 2y| – |2x – y| – xy if x = –2 and y = 7. A.–9 B.9 C.19 D.41 5–Minute Check 3

  3. Factor 8xy2 – 4xy. A.2x(4xy2– y) B.4xy(2y – 1) C.4xy(y2– 1) D.4y2(2x – 1) 5–Minute Check 4

  4. A. B. C. D. 5–Minute Check 5

  5. 1.1 Functions Splash Screen

  6. Objectives • Use Set Notation • Use Interval Notation

  7. Set – a collection of objects Example: Colors, Cars Element – are the objects that belong to a set. Example: red, orange, blue, …. Nissan, Audi, Jeep, …

  8. Infinite Set A set that has an unending list of elements Countable – a collection of objects Uncountable – are the objects that belong to a set.

  9. Key Concept 1

  10. Use Set-Builder Notation A. Describe {2, 3, 4, 5, 6, 7} using set-builder notation. The set includes natural numbers greater than or equal to 2 and less than or equal to 7. This is read as the set of all x such that 2 is less than or equal to x and x is less than or equal to 7 and x is an element of the set of natural numbers. Example 1

  11. Use Set-Builder Notation B. Describe x > –17 using set-builder notation. The set includes all real numbers greater than –17. Example 1

  12. Use Set-Builder Notation C. Describe all multiples of seven using set-builder notation. The set includes all integers that are multiples of 7. Example 1

  13. A. B. C. D. Describe {6, 7, 8, 9, 10, …} using set-builder notation. Example 1

  14. Interval Notation Is a method of writing numbers in a set. Recall the Number Line

  15. Use Interval Notation A. Write –2 ≤x ≤12 using interval notation. The set includes all real numbers greater than or equal to –2 and less than or equal to 12. Answer:[–2, 12] Example 2

  16. Answer: (–4, ) Use Interval Notation B. Write x > –4 using interval notation. The set includes all real numbers greater than –4. Example 2

  17. Answer: Use Interval Notation C. Write x < 3 or x ≥ 54 using interval notation. The set includes all real numbers less than 3 and all real numbers greater than or equal to 54. Example 2

  18. A. B. C. (–1, 5) D. Write x > 5 or x < –1 using interval notation. Example 2

  19. Review Homework

  20. 1.1 Functions Continued • What is a function? • How do we use the Vertical Line Test?

  21. x represents the domain y represents the range Key Concept 3

  22. Turn your pencil vertically. Does you pencil pass through the graph more than once? Key Concept 3a

  23. Identify Relations that are Functions B. Determine whether the table represents y as a function of x. Answer:No; there is more than one y-value for an x-value. Example 3

  24. Identify Relations that are Functions C. Determine whether the graph represents y as a function of x. Answer:Yes; there is exactly one y-value for each x-value. Any vertical line will intersect the graph at only one point. Therefore, the graph represents y as a function of x. Example 3

  25. Practice WKST

  26. Review Homework And Worksheet

  27. Quiz on Section 1.1 Tuesday, September 16 Day 4 Extra Help – Second half of Lunch

  28. 1.1 – Functions Objectives • Determine if the equation is a function • Find function values • Find the domain of the function

  29. Divide each side by 3. Take the square root of each side. Identify Relations that are Functions D. Determine whether x = 3y2 represents y as a function of x. To determine whether this equation represents y as a function of x, solve the equation for y. x = 3y2 Original equation Example 3

  30. Identify Relations that are Functions This equation does not represent y as a function of x because there will be two corresponding y-values, one positive and one negative, for any x-value greater than 0. Let x = 12. Answer:No; there is more than one y-value for an x-value. Example 3

  31. Determine whether 12x2 + 4y = 8 represents y as a function of x. A. Yes; there is exactly one y-value for each x-value. B. No; there is more than one y-value for an x-value. Example 3

  32. Find Function Values A. If f(x) = x2 – 2x – 8, find f(3). To find f(3), replace x with 3 in f(x) =x2 –2x –8. f(x) =x2 –2x –8 Original function f(3) =32–2(3) –8 Substitute 3 for x. = 9 – 6 – 8 Simplify. = –5 Subtract. Answer:–5 Example 4

  33. Find Function Values B. If f(x) = x2 – 2x – 8, find f(–3d). To find f(–3d), replace x with –3d in f(x) = x2 – 2x – 8. f(x) = x2 – 2x – 8 Original function f(–3d) = (–3d)2– 2(–3d) – 8 Substitute –3d for x. = 9d2 + 6d – 8 Simplify. Answer:9d2 + 6d – 8 Example 4

  34. Find Function Values C. If f(x) = x2 – 2x – 8, find f(2a – 1). To find f(2a – 1), replace x with 2a – 1 in f(x) = x2 – 2x – 8. f(x) = x2 – 2x – 8 Original function f(2a – 1) = (2a – 1)2– 2(2a – 1) – 8 Substitute 2a – 1 for x. = 4a2 – 4a + 1 – 4a + 2 – 8 Expand (2a – 1)2 and 2(2a – 1). = 4a2 – 8a – 5 Simplify. Answer:4a2 – 8a – 5 Example 4

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