Question

Which of the following function rules represents the graph shown?

Answer 1

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

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 $(x_2,y_2)$.

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

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

$y-0=\frac{-3-0}{0-3}(x-3)$

$y=1(x-3)$

$y=x-3$

$f(x)=x-3$

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

Answer 2

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.