The graph shown represents an absolute function.
The equation of the graph is [tex]\mathbf{y = -\frac 12|x|}[/tex]
Considering the straight on the right, we have the following points
[tex]\mathbf{(x,y) = (0,0) (4,-2)}[/tex]
Start by calculating the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{-2 - 0}{4-0}}[/tex]
[tex]\mathbf{m = \frac{-2 }{4}}[/tex]
Simplify
[tex]\mathbf{m = -\frac{1}{2}}[/tex]
So, the slope of the line is -1/2
The equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
This gives
[tex]\mathbf{y = -\frac 12(x -0) + 0}[/tex]
[tex]\mathbf{y = -\frac 12(x)}[/tex]
Represent x as an absolute value
[tex]\mathbf{y = -\frac 12|x|}[/tex]
Hence, the equation of the graph is [tex]\mathbf{y = -\frac 12|x|}[/tex]
Read more about absolute graphs at:
https://brainly.com/question/1389494
