Question

Need help with this math problem

Answer 1

`f(x)=-5x-3`.

Explanation:

From the given machine diagram it is clear that:

`f(x)=-8` at
`x=1`

`f(x)=-13` at
`x=2`

`f(x)=-18` at
`x=3`

It is clear that the value of f(x) decreasing by 5 when the value of x is increasing by 1.

Since the function changing at a constant rate, therefore it represents a linear function.

If a linear function passing through two points, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The given linear function passes through (1,-8) and (2,-13), therefore the linear equation is

`y-(-8)=(-13-(-8))/(2-1)(x-1)`

`y+8=(-5)/(1)(x-1)`

`y+8=-5(x-1)`

`y=-5x+5-8`

`y=-5x-3`

So, the required function is
`f(x)=-5x-3`.