Question

Complete the statement about the tables below. Then, choose a rule for each.

This table represents a(n) relationship

1. Exponential

2. Linear

3. Quadratic

4. Absolute value
X Y
0 5
1 7. 5
2 11. 25



By Rule: ?

1. Y= 2. 5x+5

2. Y= l1. 5x+5l

3. Y= 5(1. 5)^x

4. Y= 1. 5x^2+5


This table represents a(n) relationship
X Y

0 -6

1 12

2 30


By Rule:

1. Y= -l18xl-6

2. Y= 18x-6

3. Y= 18x^2-6

4. Y= (-2)^x-6

Answer 1

This table represents a quadratic relationship.

By Rule:

The correct choice is:

4. Y = 1.5x^2 + 5

This table represents an exponential relationship.

By Rule:

The correct choice is:

3. Y = 18x^2 - 6

Explanation:

Answer 2

For the first table:

The relationship represented by the table is an exponential relationship. This can be determined by observing that as the value of X increases by 1, the value of Y increases by a constant factor of 1.5. In an exponential relationship, the dependent variable (Y) changes by a constant ratio or factor as the independent variable (X) changes.

By Rule:

The correct rule that represents the relationship in the first table is option 3: Y = 5(1.5)^x. This rule accurately shows that the value of Y is determined by multiplying 5 with 1.5 raised to the power of X.

For the second table:

The relationship represented by the table is a linear relationship. This can be determined by observing that as the value of X increases by 1, the value of Y increases by a constant amount of 18. In a linear relationship, the dependent variable (Y) changes by a constant amount as the independent variable (X) changes.

By Rule:

The correct rule that represents the relationship in the second table is option 2: Y = 18x - 6. This rule accurately shows that the value of Y is determined by multiplying 18 with X and then subtracting 6.