Question

1. give the domain and range of the relation.

x	y
3	7
6	13
0	0
-7	-13

a. d: {3, 6, -7, 7, 13, -13}; r: {0} c. d: {-7, 3, 6}; r: {-13, 7, 13}
b. d: {-7, 0, 3, 6}; r: {-13, 0, 7, 13} d. d: {-13, 0, 7, 13}; r: {-7, 0, 3, 6}

1. when solving the equation, what property was used to go from step 2 to step 3?

step 1: -(2x + 3) = x - 18
step 2: -2x - 3 = x - 18
step 3: -3 = 3x - 18
a. addition property of equality c. multiplication property of equality
b. subtraction property of equality d. division property of equality

Explanation:

Question 45

Step1: Recall domain/range definitions

Domain (D) is set of all \( x \)-values, Range (R) is set of all \( y \)-values from the relation.
From the table: \( x \)-values are \( 3, 6, 0, -7 \); \( y \)-values are \( 7, 13, 0, -13 \).

Step2: Match with options

• Option a: Incorrect (mixes \( x \) and \( y \) values).
• Option b: \( D = \{-7, 0, 3, 6\} \), \( R = \{-13, 0, 7, 13\} \) (matches \( x \) and \( y \) sets).
• Option c: Missing \( x = 0 \), missing \( y = 0 \), \( 7, 13 \) incomplete.
• Option d: Swaps domain and range.

Step1: Analyze Step 2 to Step 3

Step 2: \( -2x - 3 = x - 18 \)
Step 3: \( -3 = 3x - 18 \)
This is adding \( 2x \) to both sides (Addition Property of Equality: if \( a = b \), then \( a + c = b + c \), here \( c = 2x \)).

Step2: Match with properties

• Option a: Addition Property (adding \( 2x \) to both sides).
• Option b: Subtraction Property (not subtracting, but adding).
• Option c: Multiplication Property (no multiplication).
• Option d: Division Property (no division).

Answer:

b. D: \(\{-7, 0, 3, 6\}\); R: \(\{-13, 0, 7, 13\}\)

Question 46