Drill #58 Express the relation shown in the table as: 1.A graph 2.a set of ordered pairs 3.mapping then find the 4.Inverse ( I = { } ) 5.Domain ( D = { } ) 6.Range (R = { } ) xy

5-3 Equations as Relations Objective: To determine the range for a given domain, and to graph the solution set for the given domain

Physical Science Open books to page 271. Are you as “light” as a feather or as “heavy” as a rock? …

(14). Equation in two variables ** Definition: An equation that contains two unknown variables. Examples:

Perimeter of a square The formula for the perimeter of a square is P=4s What ordered pairs (s, P) make this equation true? Find the perimeter if the square has side length of {1, 2, 2.5, 3} SPOrdered Pair (s, P)

Perimeter of a square Substitute values of s into the equation to find values of P. The ordered pairs (s,P) that satisfy the equation P=4s are the solution set. sPOrdered Pair 14(1,4) 28(2,8) 2.510(2.5,10) 312(3,12)

(15). Solution of an Equation in Two Variables ** If a true statement results when the numbers in an ordered pair are substituted into an equation in two variables, then the ordered pair is a solution of the equation. Example: The ordered pair (1,2) is a solution to the equation y = 2x.

Find the solution set (CW #58*) If y = 4x and the domain is {-3, -2, 0, 1, 2} Make a table. Substitute the values in the domain for x. Domain (x) 4(x) Range (y)Ordered Pair -34(-3) -24(-2) 04(0) 14(1) 24(2)

Find the solution set If y = 4x and the domain is {-3, -2, 0, 1, 2} Make a table. Substitute the values in the domain for x. Solution = { (-3, -12), (-2, -8), (0, 0), (1, 4), (2, 8) } Domain (x) 4(x)Range (y)Ordered Pair -34(-3)-12(-3,-12) -24(-2)-8(-2,-8) 04(0)0(0,0) 14(1)4(1,4) 24(2)8(2,8)

Find the solution set (CW #58*) If y = x + 6 and the range is { 2, 3, 5, 8, 10} Make a table. Substitute the values in the domain for x. Domain (x) x = ?y (range)Ordered Pair

Find the solution set If y = x + 6 and the domain is {-4, -3, -1, 2, 4} Make a table. Substitute the values in the domain for x. Solution = { (-4, 2), (-3, 3), (-1, 5), (2, 8), (4, 10) } x x = y – 6yOrdered Pair -42 – 62(-4,2) -33 – 63(-3,3) 5 – 65(-1,5) 28 – 68(2,8) 410 – 610(4,10)

Find the solution set given the domain If 4x + 2y = 12 and the domain is {-2, 0, 5, 8}

Find the solution set given the domain (solve for y) If 4x + 2y = 12 and the domain is {-2, 0, 5, 8} Solve for y first… 4x + 2y – 4x = 12 – 4x (subtract 4x from both sides) 2y = 12 – 4x (divide both sides by 2) 2y = 12 – 4x 2 y = 12 – 4xReduce the fraction 2 2 y = 6 – 2x

Find the solution Next make a table… substitute the domain values for x… find the values of y, and the ordered pair (x,y) Domain (x) 6 – 2xYOrdered Pair -26 – 2(-2) 06 – 2(0) 56 – 2(5) 86 – 2(8)

Find the solution set Next make a table… substitute the domain values for x… find the values of y, and the ordered pair (x,y) Solution = { ( -2, 10), (0, 6), (5, -4), (8, -10) } Domain (x) 6 – 2xYOrdered Pair -26 – 2(-2)10(-2, 10) 06 – 2(0)6(0, 6) 56 – 2(5)-4(5,-4) 86 – 2(8)-10(8,-10)

Class-work #7-11 Pg