Choose the most appropriate equation for the function drawn as a thick line,…
2015
Choose the most appropriate equation for the function drawn as a thick line, in the plot below.
- A.
\(x=y-|y|\) - B.
\(x=-(y-|y|)\) - C.
\(x=y+|y|\) - D.
\(x=-(y+|y|)\)
Attempted by 77 students.
Show answer & explanation
Correct answer: B
Interpretation of the plot: the thick curve is a vertical segment along x = 0 for nonnegative y (it goes up along the y-axis from the origin) and for negative y it is a straight line passing through the origin and going down-right (for example the point (2,-1) lies on this line).
Check the candidate expression x = -(y - |y|) piecewise:
For y >= 0: |y| = y, so x = -(y - y) = 0. This gives the vertical segment on x = 0 for nonnegative y, as seen on the plot.
For y < 0: |y| = -y, so x = - (y - (-y)) = - (2y) = -2y. Rearranged, y = -x/2 for these points, which is a line with negative slope passing through the origin and going down-right for positive x (so at x = 2, y = -1).
Conclusion: x = -(y - |y|) produces exactly the vertical segment for y >= 0 and the down-right line for y < 0 that match the plotted thick curve, so this is the correct equation.
Quick checks of the other candidate expressions show they produce the vertical segment on the wrong side or a diagonal in the wrong direction, so they do not match the plot.