Drill #58

Express the relation shown in the table as:1. A graph2. a set of ordered pairs3. mapping

then find the 4. Inverse ( I = { } )5. Domain ( D = { } )6. Range (R = { } )

x y

2 1

3 -3

-1 1

3 2

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:

rC 2sP 42sA3sV

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} S P Ordered Pair (s, P)

1

2

2.5

3

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.

s P Ordered Pair

1 4 (1,4)

2 8 (2,8)

2.5 10 (2.5,10)

3 12 (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

-3 4(-3)

-2 4(-2)

0 4(0)

1 4(1)

2 4(2)

Find the solution setIf 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

-3 4(-3) -12 (-3,-12)

-2 4(-2) -8 (-2,-8)

0 4(0) 0 (0,0)

1 4(1) 4 (1,4)

2 4(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

2

3

5

8

10

Find the solution setIf 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 – 6 y Ordered Pair

-4 2 – 6 2 (-4,2)

-3 3 – 6 3 (-3,3)

-1 5 – 6 5 (-1,5)

2 8 – 6 8 (2,8)

4 10 – 6 10 (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 2

y = 12 – 4x Reduce the fraction

2 2

y = 6 – 2x

Find the solutionNext make a table…

substitute the domain values for x…

find the values of y, and the ordered pair (x,y)

Domain (x) 6 – 2x Y Ordered Pair

-2 6 – 2(-2)

0 6 – 2(0)

5 6 – 2(5)

8 6 – 2(8)

Find the solution setNext 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 – 2x Y Ordered Pair

-2 6 – 2(-2) 10 (-2, 10)

0 6 – 2(0) 6 (0, 6)

5 6 – 2(5) -4 (5,-4)

8 6 – 2(8) -10 (8,-10)

Class-work

#7-11 Pg 274-275