The set of ordered pairs represents a function. Write a rule that represents the function. (0,0) (1,2) (2,8) (3,18) (4,32)

The function can be y = 2x²

Step-by-step explanation:

Hi there!

Let's write a generic function:

y = a · xⁿ + b

Replacing x and y for the pairs of values, we obtain the following system of equations:

(0,0)

0 = a ·0ⁿ + b ⇒ 0 = b

(1,2)

2 = a · 1ⁿ + b

(2,8)

8 = a · 2ⁿ + b

(3,18)

18 = a · 3ⁿ + b

(4,32)

32 = a · 4ⁿ + b

From the first equation, we obtain that b = 0

From the second equation:

2 = a · 1ⁿ

divide by 1ⁿ both sides of the equation:

2/1ⁿ = a

2 = a

From the third equation:

18 = a · 3ⁿ + b

18 = 2 · 3ⁿ

divide by 2 both sides of the equation

9 = 3ⁿ

n = 2

Let's check if these values of a, b and n satify the other pair:

32 = a · 4ⁿ + b

32 = 2 · 4² + 0

32 = 2 · 16

32 = 32

Then, the function is

y = 2 · x²