+2446 If we assume that "the graph consists of three line segments," then we can generate the equation of the lines.
Of course, I could use \(y=mx+b\), but that would require me to know the y-intercept of the first red line, and, unfortunately, the y-intercept is not clear-cut in the image.
I will use point-slope form instead; this form requires me to know the coordinates of any two points on that line. \(y-y_1=m(x-x_1)\) is the form of point-slope form. \((x_1,y_1)\) is the coordinate of any one point of the line. In the image, I can pinpoint that \((-4,4)\text{ and }(-1,-1)\) both lie on the line I care about for this problem. Now that they are identified, I can now find the slope.
\(m=\frac{-1-4}{-1-(-4)}=\frac{-5}{3}\)
I will substitute in the point \((-1,-1)\) as my point.
Since we are trying to find \(f(-2)\) , x=-2.
| \(y_1=-1;m=-\frac{5}{3};x=-2;x_1=-1\\ y-y_1=m(x-x_1)\\ y-(-1)=-\frac{5}{3}(-2-(-1))\) | It is time to solve for y! |
| \(y+1=-\frac{5}{3}*-1\\ y+\frac{3}{3}=\frac{5}{3}\\ y=\frac{2}{3}\) | |
\(f(-2)=\frac{2}{3}\). You will see that this answer is consistent with the initially given diagram.
