Question

Which of the following function rules represents the graph shown?

f(x) = x - 3

f(x) = 3 - x

f(x) = -3x

Answer 1

As the line raises from left to right, the slope must be positive, so only the function, f(x)=x-3, has a slope greater than zero. Additionally, at x=0, the y-value is at, or around, -3, confirming that f(x)=x-3 is the correct solution. 

Answer 2

Answer: The correct option first, i.e., f(x)=x-3.

Step-by-step explanation:

From the given graph it is noticed that the y intercept of the line is (0,-3) and the x intercept of the line is (3,0).

The equation of line which passing through two points
`(x_1,y_1)` and
`(x_2,y_2)`.

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

The equation of line passing through (3,0) and (0,-3),

`y-0=(-3-0)/(0-3)(x-3)`

`y=1(x-3)`

`y=x-3`

`f(x)=x-3`

Therefore the correct option is first, i.e., f(x)=x-3.