Which of the following function rules represents the graph shown?f(x) = x-3f(x) = 3 -f(x) = -3x

Accepted Solution

Answer:[tex]y=f(x)=x-3[/tex]Step-by-step explanation:The given graph is attached.In the graph, you can observe that the linear function has interception with x-axis and y-axis at points (3,0) and (0,-3).So, the right function among the options must be satisfied by these two points. We already now that the third option is not the right answer because it doesn't have the independent term which indicates the interception with the vertical axis.To get the most accurate answer, and demonstrate all the process at the same time, we first could fin the slope and then use the point-slope form to find the right function:[tex]m=\frac{-3-0}{0-3}=\frac{-3}{-3}=1[/tex][tex]y-y_{1}=m(x-x_{1})\\y-0=1(x-3)\\y=x-3[/tex]Therefore, the first option fits the equation. So, the right answer is[tex]y=f(x)=x-3[/tex]