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Find the value of x 2 + 4x + 4 if x = –2. A. –8 B. 0 C. 4 D. 16 Evaluate |x – 2y| – |2x – y| – xy if x = –2 and y = 7. A. –9 B. 9 C. 19 D. 41 Factor 8xy 2 – 4xy. A. 2x(4xy 2 – y) B. 4xy(2y – 1) C. 4xy(y 2 – 1) D. 4y 2(2x – 1) A. B. C. D. 1.1 Functions Objectives • Use Set Notation • Use Interval Notation Set – a collection of objects Example: Colors, Cars Element – are the objects that belong to a set. Example: red, orange, blue, …. Nissan, Audi, Jeep, … 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. 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. Use Set-Builder Notation B. Describe x > –17 using set-builder notation. The set includes all real numbers greater than –17. Use Set-Builder Notation C. Describe all multiples of seven using set-builder notation. The set includes all integers that are multiples of 7. Describe {6, 7, 8, 9, 10, …} using set-builder notation. A. B. C. D. Interval Notation Is a method of writing numbers in a set. Recall the Number Line 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] Use Interval Notation B. Write x > –4 using interval notation. The set includes all real numbers greater than –4. Answer: (–4, ) 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. Answer: Write x > 5 or x < –1 using interval notation. A. B. C. (–1, 5) D. Review Homework 1.1 Functions Continued • What is a function? • How do we use the Vertical Line Test? x represents the domain y represents the range Turn your pencil vertically. Does you pencil pass through the graph more than once? 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. 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 xvalue. Any vertical line will intersect the graph at only one point. Therefore, the graph represents y as a function of x. Practice WKST Review Homework And Worksheet Quiz on Section 1.1 Tuesday, September 16 Day 4 Extra Help – Second half of Lunch 1.1 – Functions Objectives • Determine if the equation is a function • Find function values • Find the domain of the function Identify Relations that are Functions D. Determine whether x = 3y 2 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 = 3y 2 Original equation Divide each side by 3. Take the square root of each side. 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. Determine whether 12x 2 + 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. Find Function Values A. If f(x) = x 2 – 2x – 8, find f(3). To find f(3), replace x with 3 in f(x) = x 2 – 2x – 8. f(x) = x 2 – 2x – 8 Original function f(3) = 3 2 – 2(3) – 8 Substitute 3 for x. =9–6–8 Simplify. = –5 Subtract. Answer: –5 Find Function Values B. If f(x) = x 2 – 2x – 8, find f(–3d). To find f(–3d), replace x with –3d in f(x) = x 2 – 2x – 8. f(x) = x 2 – 2x – 8 f(–3d) = (–3d)2 – 2(–3d) – 8 = 9d 2 + 6d – 8 Answer: 9d 2 + 6d – 8 Original function Substitute –3d for x. Simplify. 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) = x 2 – 2x – 8. f(x) = x 2 – 2x – 8 f(2a – 1) = (2a – 1)2 – 2(2a – 1) – 8 Original function Substitute 2a – 1 for x. = 4a 2 – 4a + 1 – 4a + 2 – 8 Expand (2a – 1)2 and 2(2a – 1). = 4a 2 – 8a – 5 Answer: 4a 2 – 8a – 5 Simplify.