Question

X f(x)

0 -2,
2 4,
6 16

What is the value of f(3)?

Answer 1

`f(3)=7`

Explanation:

Given:

`x`
`f(x)`

0 -2

2 4

6 16

Let us first determine whether the rate of change of the function is constant or not.

The rate of change of the function is given as:

`m=(f(x_2)-f(x_1))/(x_2-x_1)`

So, for
`x_1=0,f(0)=-2,x_2=2,f(2)=4`

`m=(4-(-2))/(2-0)=(4+2)/(2)=(6)/(2)=3`

For the next set of numbers,
`x_2 = 2, f(2)=4,x_3=6,f(6)=16`

`m=(16-4)/(6-2)=(12)/(4)=3`

Therefore, the rate of change of the function is a constant. Therefore, the relationship is a linear relationship.

A linear relationship with a given point
`(x_1,y_1)` and constant rate of change
`m` is given as:

`y-y_1=m(x-x_1)\\y-(-2)=3(x-0)\\y+2=3x\\y=3x-2\\\therefore f(x)=3x-2`

Now, value of
`f(3)` is obtained by plugging in 3 for
`x` in the above expression.

`f(3)=3(3)-2\\f(3)=9-2=7`