HOW TO FIND THE DOMAIN AND RANGE OF A RELATION GRAPH

Problem 1 :

Identify the values of the domain for the following relation :

A) {-2, 0, 1, 3}        B) {-3, -2, 0, 1, 2}

C) {-2, -1, 0, 1, 2, 3}     D) {-3, 0, 1, 2} 

Solution :

From the given graph,

A (2, 1), B (-3, -2), C (0, 3) and D (1, 0)

The domain of a relation is the set of x values of the ordered pairs.

Domain = {2, -3, 0, 1}

Domain = {-3, 0, 1, 2}

So, option (D) is correct.

Problem 2 :

Identify the values for the domain of the function :

A)  {-2, -1, 0, 1, 2}

B) {(1, -2), (-1, -1), (2, 0), (1, 1), (2, 2)}

C) {-1, 1, 2}

D) {(-2, 1), (-1, -1), (0, 2), (1, 1), (2, 2)}

Solution :

From the given graph,

A (2, 2), B (1, 1), C (0, 2), D (-2, 1) and (-1, -1)

The domain of a relation is the set of x values of the ordered pairs.

Domain = {2, 1, 0, -2, -1}

Domain = {-2, -1, 0, 1, 2}

So, option (A) is correct.

Problem 3 :

List the range for the following function.

{(2, 3), (4, 5), (3, 4), (7, 8)}

A) {3, 4, 5, 8}           B) {2, 3, 4, 7}

C) {2, 3, 4, 5, 7, 8}       D) {2, 3, 3, 4, 4, 5, 7, 8}

Solution :

The range of a relation is the set of y values of the ordered pairs.

Range = {3, 5, 4, 8}

Range = {3, 4, 5, 8}

So, option (A) is correct.

Problem 4 :

Identify the values of the range for the following relation :

{(2, 3), (5, 7), (7, 9), (4, 8)}

A) {2, 5, 7, 4}             B) {2, 3, 4, 8}

C) {2, 8}                     D) {3, 7, 9, 8}

Solution :

The range of a relation is the set of y values of the ordered pairs.

Range = {3, 7, 9, 8}

So, option (D) is correct.

Problem 5 :

Identify the range for the following relation :

A) {-2, -1, 3, 5}                    B) {-1, 0, 4, 7}

C) {-2, -1, 0, 3, 4, 5, 7}           D) {0, 1, 4, 7}

Solution :

Range = {4, 0, -1, 7}

So, option (B) is correct.

Problem 6:

To graph the equation y = 3x - 7,

Renita created the following table of values.

Which y -value corresponds to 7?

A)   21    B)  28      C) 14      D)  -4

Solution :

y = 3x - 7

Put x = 7,

y = 3(7) - 7

y = 21 - 7

y = 14

So, option (C) is correct.

Problem 7 :

A relation is graphed as shown.

Find all the values that are in the domain of this relation.

Solution :

From the given graph,

(1, 6), (3, 3), (4, 2), (6, 5)

Domain = {1, 3, 4, 6}

Problem 8 :

Florida’s state marine mammal is the manatee. A manatee eats about 12% of its body weight each day.

a. Write an equation in function form that represents the amount y (in pounds) of food a manatee eats each day for its weight x.

b. Create an input-output table for the equation in part (a). Use the inputs 150, 300, 450, 600, 750, and 900.

c. Find the domain and range of the function represented by the table.

d. An aquatic center has manatees that weigh 300 pounds, 750 pounds, and 1050 pounds. How many pounds of food do all three manatees eat in a day? in a week?

Solution :

x - amount of manatee eats each day for its weight

y - amount of food

a) y = 12% of x

= (12/100) x

y = 0.12x

b) 

c)

d)

Problem 9 :

The number of earrings and headbands you can buy with $24 is represented by the equation 8x + 4y = 24. The table shows the number of earrings and headbands.

a. Write the equation in function form.

b. Find the domain and range.

c. Why is x = 6 not in the domain of the function?

Solution :

a) y-intercept = 6

Slope = (y₂ - y₁)/(x₂ - x₁)

= (4 - 6) / (1 - 0)

= -2/1

= -2

y = mx + b

y = -2x + 6

b) Domain = {0, 1, 2, 3}

Range = {6, 4, 2, 0}

c) When x = 6

8x + 4y = 24

8(6) + 4y = 24

48 + 4y = 24

4y = 24 - 48

4y = -24

y = -24/4

y = -6

Since we get the negative value that is number of headbands. So, x = 6 cannot be in the domain.