Question: Choose the graphs that represent the graphs of inverses. Select one or more: a. b. Graph a: two S-shaped curves that are mirror images across the line $y = x$; one curve is steep and vertical-like near the center, and the other is its horizontal reflection, position_hint=center. Graph b: two curves that are not mirror images across the line $y = x$; one dark curve rises from left to right while the red curve slopes downward, position_hint=bottom-center. c. Two parabolas are shown on the coordinate plane. The black parabola is in the top-right quadrant, opens upward, and has its vertex on the x-axis to the right of the y-axis. The red parabola is in the bottom-left quadrant, opens downward, and has its vertex on the x-axis to the left of the y-axis. position_hint=top-right d. Two lines are shown on the coordinate plane. The black line has a gentle positive slope and crosses the y-axis slightly below the x-axis. The red line has a steeper positive slope and crosses the y-axis above the x-axis. position_hint=bottom-right

1. **Problem Statement:** Identify which graphs represent pairs of inverse functions. 2. **Key Concept:** Two functions $f$ and $g$ are inverses if and only if their graphs are symmetric with respect to the line $y = x$. 3. **Step-by-step Analysis:** 1. **Graph a:** The two S-shaped curves are mirror images across the line $y = x$. This symmetry indicates that these two curves are inverses of each other. 2. **Graph b:** The two curves are not mirror images across the line $y = x$. Therefore, they are not inverses. 3. **Graph c:** The two parabolas are located in opposite quadrants and open in opposite directions but are not symmetric about $y = x$. Parabolas generally do not have inverses that are functions unless restricted, and these are not symmetric about $y = x$. 4. **Graph d:** Two lines with different slopes and y-intercepts are shown. For two lines to be inverses, they must be symmetric about $y = x$. Without that symmetry, they are not inverses. 4. **Conclusion:** Only graph a shows two functions that are inverses of each other. **Final answer:** Graph a represents the graphs of inverses.