1. **Stating the problem:** We are given six different graphs with points labeled on their axes and curves. The task is to analyze the first graph, which is a cubic function with points labeled on the x-axis as $-1$, $0$, $1$ and points on the curve as $a$, $b$. 2. **Understanding cubic functions:** A cubic function generally has the form $$y = ax^3 + bx^2 + cx + d$$ where $a \neq 0$. 3. **Key properties:** Cubic functions can have up to three real roots and can have one or two turning points (local maxima or minima). 4. **Given points:** The x-axis points are $-1$, $0$, and $1$. The curve points $a$ and $b$ correspond to the function values at some x-values. 5. **Evaluating the function at given points:** Suppose the function is $$y = -x^3 - 2x$$ (inferred from the labels in the problem statement). 6. **Calculate $y$ at $x = -1$:** $$y = -(-1)^3 - 2(-1) = -(-1) + 2 = 1 + 2 = 3$$ 7. **Calculate $y$ at $x = 0$:** $$y = -(0)^3 - 2(0) = 0$$ 8. **Calculate $y$ at $x = 1$:** $$y = -(1)^3 - 2(1) = -1 - 2 = -3$$ 9. **Assigning $a$ and $b$:** From the calculations, $a = y(-1) = 3$ and $b = y(1) = -3$. 10. **Summary:** The cubic function is $$y = -x^3 - 2x$$ with points $a = 3$ and $b = -3$ on the curve at $x = -1$ and $x = 1$ respectively. This shows how to evaluate a cubic function at specific points and interpret the values on the graph. Final answer: $$y = -x^3 - 2x, \quad a = 3, \quad b = -3$$