Question

Describe a relationship that can be modeled by the function shown in the table, and explain how the function models the relationship.

x f(x)
1 4
4 8
9 12
16 16
25 20

Answer 1

y = 4·√x

Explanation:

f(x) is defined as a product of 4 into √x

4 × √1 = 4

4 × √4 = 8

4 × √9 = 12

4 × √16 = 16

4 × √25= 20

Hence, the relationship is defined as : y is 4 times the square root of x

i.e. y = f(x) = 4·√x

Answer 2

f(x) is 4 times the square root of x

Explanation:

4 × √1 = 4

i.e. f(1)=4·√1

4 × √4 = 8

i.e. f(4)=4·√4

4 × √9 = 12

i.e. f(9)=4·√9

4 × √16 = 16

i.e. f(16)=4·√16

4 × √25= 20

i.e. f(25)=4·√25

As we can clearly see, f(x) is 4 times the square root of x

i.e. f(x) = 4·√x