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Feb 16, 2019

#1
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Feb 16, 2019
#2
+2419
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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.

Feb 16, 2019