Circles & Interval & Set Notation.notebook. November 16, 2009 CIRCLES. OBJECTIVE Graph a Circle given the equation in standard form.

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1 OBJECTIVE Graph a Circle given the equation in standard form. Write the equation of a circle in standard form given a graph or two points (one being the center). Students will be able to write the domain and range in Students will be able to write the domain and range in set builder notation. CIRCLES Standard Form of a Circle (x h) 2 + (y k) 2 = r 2 where (h, k) is the center of the circle where r is the radius of the circle To Graph: Plot the center. Place 4 points using the radius. Connect the points. Oct 11 10:40 AM Nov 16 11:15 AM (x 5) 2 + (y 3) 2 = 16 (x + 1) 2 + (y 4) 2 = 9 Center: Center: Radius: Radius: Nov 16 11:15 AM Nov 16 11:18 AM Write the equation of the circle. Write the equation of the circle. Nov 16 11:18 AM Nov 16 11:21 AM 1

2 Write the equation of the circle given the Center of ( 3, 7) and a Point on the Circle of (1, 10). Write the equation of the circle given the Center of (1, 6) and a Point on the Circle of ( 3, 6). Nov 16 11:21 AM Nov 16 11:22 AM x 5 x< Solid Dots in Interval Notation are brackets [ or ]. Describe the graph in interval notation as you read the graph from left to right. [ 5, + ) Greater than sign will always have + ) on the right side of the Open Circles in Interval Notation are parenthesis ( or ). Describe the graph in interval notation as you read the graph from left to right. (, 2 ) Less than sign will always have ( - on the left side of the Oct 11 10:41 AM Oct 11 10:53 AM x - 6 and x< 2 Write the interval notation for each inequality separately. x - 6 x< 2 [ - 6, + ) ( -, 2 ) means "and" also called a "union" also called a "conjunction" means "or" also called a "disjunction" Solid Dots in Interval Notation are brackets [ or ]. Greater than sign will always have + ) on the right side of the Open Circles in Interval Notation are parenthesis ( or ). Less than sign will always have ( - on the left side of the means "and" also called a "union" also called a "conjunction" means "or" also called a "disjunction" [ - 6, + ) ( -, 2 ) Oct 11 10:57 AM Oct 11 11:05 AM 2

3 1) x 4 (8, 5) 2) x - 3 3) x < 7 4) x > - 1 (-8, -2) 5) x 0 or x 2 6) x > 5 and x < 8 7) x > - 6 and x 7 Oct 11 11:07 AM Nov 16 10:50 AM Nov 16 10:53 AM Nov 16 12:09 PM A set is a well defined collection of objects called members or elements. We will use capital letters to represent sets. The letter B is commonly used to represent the set of whole numbers. The letter Z is commonly used to represent the set of integers. The letter Q is commonly used to represent the set of rationals. The letter R is commonly used to represent the set of all reals. The symbol means "is an element of" and the symbol means "is not an element of". Oct 11 11:11 AM Oct 11 11:23 AM 3

4 such that { x x is a whole number and x > 20 } 1) the set C of whole numbers greater than 5 C = { x x is a whole number and x > 5} Variable Description 2) the set N of negative integers We read this as " the set of all x such that x is a whole number and x is greater than 20". N = { x x is an integer and x < 0} Oct 11 11:28 AM Oct 11 11:35 AM 1) the set B of whole numbers less than 7 2) the set E of positive integers The intersection of two sets A and B, written A B, the set of all members that are common to both sets. A B is read "A intersection B". 3) the set G of whole numbers greater than 5 4) the set T of multiples of 5 less than 24 A B 5) the set P of prime numbers less than 20 Set A Set B Oct 11 11:32 AM Oct 11 11:41 AM The intersection of two sets A and B, written A B, the set of all members that are common to both sets. A B is read "A intersection B". Let E be the set of even numbers. Let W be the set of whole numbers. Let T = { 0, 2 }. Let S = { 1, 5 }. 1) Find S T. 2) Find E W. E Even Numbers Odd Numbers 3) Find T E. 4) Find E S. { 0, 2} or T If there are no members common to both sets. Thus the intersection is empty. We say the intersection is the "empty set", which is symbolized by { } or. 5) Find W S. 6) Find W T. S T Oct 11 11:52 AM Oct 11 11:56 AM 4

5 (8, 5) (-8, -2) Oct 11 12:17 PM Nov 16 10:56 AM Nov 16 12:55 PM 5