1. The problem asks to find the locations of discontinuities for four different graphs described. 2. Discontinuities in functions often occur where the function is undefined, such as vertical asymptotes, holes (removable discontinuities), or jump discontinuities. 3. For the top-left graph: It is a rational function with two vertical asymptotes and a horizontal asymptote along the x-axis. Vertical asymptotes indicate discontinuities where the denominator is zero and the function tends to infinity. 4. For the top-right graph: It is a piecewise function with a jump discontinuity at the origin (0), where the function changes from a decreasing line to a rising segment with a filled point, and then a curve with an open circle indicating a discontinuity. 5. For the bottom-left graph: It is a rational function with one vertical asymptote left of the y-axis, indicating a discontinuity at that x-value. 6. For the bottom-right graph: It is a decreasing line segment with an open circle near the left end, indicating a discontinuity at that point. 7. Summarizing the locations: - Top-left graph discontinuities: at the two vertical asymptotes (call them $x=a$ and $x=b$). - Top-right graph discontinuity: at $x=0$ (jump and open circle). - Bottom-left graph discontinuity: at the vertical asymptote $x=c$ (left of y-axis). - Bottom-right graph discontinuity: at the open circle point $x=d$ (near left end). Since exact numeric values are not given, the discontinuities are at these characteristic points. Final answer: $$\text{Top-left: } x=a, x=b$$ $$\text{Top-right: } x=0$$ $$\text{Bottom-left: } x=c$$ $$\text{Bottom-right: } x=d$$